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In her solo performance, Knot in My Name, Ita Segev utilizes transaesthetic strategies and technology to elucidate her mutually dependent investments in gender and nation and the urgent personal and political stakes of the ongoing Israeli occupation for the performer and her American audience alike.

This essay reviews the following works: La marchita, el escudo y el bombo: Una historia cultural de los emblemas del peronismo, de Peron a Cristina Kirchner. By Ezequiel Adamovsky and Esteban Buch. Buenos Aires: Planeta, 2016. Pp. 367. ARS$555 paperback. ISBN: 9789504954750. The Resurgence of Populism in Latin America. By Robert R. Barr. Boulder, CO: Lynne Rienner, 2017. Pp. xii + 251. $75 hardcover. ISBN: 9781626376670. The Promise and Perils of Populism: Global Perspectives. Edited by Carlos de la Torre. Lexington: University Press of Kentucky, 2015. Pp. viii + 474. $45.00 paperback. ISBN: 9780813153308. Latin America’s Leaders. By Rut Diamint and Laura Tedesco. London: Zed, 2015. Pp. xi + 188. $25.00 paperback. ISBN: 9781783601028. Evita, Inevitably: Performing Argentina’s Icons before and after Eva Peron. By Jean Graham-Jones. Ann Arbor: University of Michigan Press, 2014. Pp. ix + 271. $37.95 paperback. ISBN: 9780472052332. Creating Charismatic Bonds in Argentina: Letters to Juan and Eva Peron. By Donna J. Guy. Albuquerque: University of New Mexico Press, 2016. Pp. vii + 173. $29.95 paperback. ISBN: 9780826338389. Populism and Performance in the Bolivarian Revolution of Venezuela. By Angela Marino. Evanston, IL: Northwestern University Press, 2018. Pp. xi + 212. $34.95 paperback. ISBN: 9780810136731. Populism: A Very Short Introduction. By Cas Mudde and Cristobal Rovira Kaltwasser. Oxford: Oxford University Press, 2017. Pp. 136. $11.95 paperback. ISBN: 9780190234874. Dancing Jacobins: A Venezuelan Genealogy of Latin American Populism. By Rafael Sanchez. New York: Fordham University Press, 2016. Pp. ix + 393. $35 paperback. ISBN: 9780823263660. When Democracy Trumps Populism: European and Latin American Lessons for the United States. Edited by Kurt Weyland and Raul L. Madrid. Cambridge: Cambridge University Press, 2019. Pp. 238. $27.99 paperback. ISBN: 9781108728829.

We give a generators-and-relations description of differential graded algebras recently introduced by Ozsváth and Szabó for the computation of knot Floer homology. We also compute the homology of these algebras and determine when they are formal.

The Burau representation of the braid group can be used to recover the Alexander polynomial of the closure of a braid. We define twisted Burau maps and use them to compute twisted Alexander polynomials., 20 pages, 3 figures; v2: minor changes, to appear in Proc. Edinburgh Math. Soc

This article argues for a shift in our thinking about racism. There are two main philosophical approaches at present: the moral view, which analyses racism in terms of individuals' attitudes, and the political view, which analyses it in terms of institutions. But neither is fully satisfactory. So I propose an alternative, genealogical account, which is better equipped to explain the phenomena associated with racism and is more in line with the historical record.

A killer of a group$G$is an element that normally generates$G$. We show that the group of a cable knot contains infinitely many killers such that no two lie in the same automorphic orbit.

Forty years ago, I contributed my first independent article to Volume 1 ofByzantine and Modern Greek Studies, ‘The lament of the Virgin in Byzantine literature and modern Greek folksong’. For this fortieth anniversary issue, dedicated to A. A. M. Bryer, I have, as in the closing words of Theodore Prodromos’ seventh letter to Aristenos (Πεϱὶ Γλώττης), nothing to offer but μικϱαῖς ἀντιδεξιοῦσα σταγόσι, καὶ ταύταις θολεϱαῖς (‘meagre and murky drops’),1further sullied with speculation on possible meanings of a single rare word:skordapsos. Does it mean ‘gut-knot’ or ‘eyesore’? Is it a vulgar form ofchordapsos, an affliction of the intestines (attested in early medical texts)? Or is it a later vernacular term for ‘eye disease’, for which garlic (skordo) was, and remains, a known curative? And does it matter?

We have the power of choice over nuclear weapons. But we do not feel our power. Instead, we feel their power. They are larger than life. They loom over us, seemingly beyond our control, shrouded in myth and dark mystery. Because of their power and our feeling that nuclear weapons are unique, we believe that these weapons require a special set of moral rules, specially tuned to the separate world where nuclear weapons dwell.

Recently, Dasbach, Futer, Kalfagianni, Lin and Stoltzfus extended the notion of a Tait graph by associating a set of ribbon graphs (or, equivalently, cellularly embedded graphs) to a link diagram. Here we focus on Seifert graphs, which are the ribbon graphs of a knot or link diagram that arise from Seifert states. We provide a characterization of Seifert graphs in terms of Eulerian subgraphs. This characterization can be viewed as a refinement of the fact that Seifert graphs are bipartite. We go on to examine the family of ribbon graphs that arises by forming the parallels of a link diagram and determine how the genus of the ribbon graph of ar-fold parallel of a link diagram is related to that of the original link diagram.

Two conflicting theories put the introduction of bronze into Southeast Asia 1000 years apart, one (before China) at 2000 BC, the other at 1000 BC. Both were drawn from radiocarbon dates, the first of pottery, the second of bone. The authors cut the Gordian Knot by showing the earlier dates to be unreliable — but their study has implications way beyond Thailand. The direct dating of pottery, it seems, is full of pitfalls…

Ever closer gets the net of networks, and so it does in law and legal scholarship. Finally in the law, one feels tempted to remark. But there is a reason for the lawyer's patient scepticism, for her professional habit to await a certain academic consolidation of a concept before setting out on a transdisciplinary transfer. There is a reason – and it lies in the law's “necessity to decide” (Entscheidungsnotwendigkeit). There is no shortage of fuzziness and uncertainty. But have life and law ever been less paradoxical? Arguably, the problem is not new, yet it has only recently been made explicit.

This article explores how the legal arguments in favour of same-sex marriage recognition in the United States and Canada have been taken up in two recent documentaries on the subject: Tying the Knot: The Union That’s Dividing America (USA, 2004) and The End of Second Class (Canada, 2006). My interest in these films lies in how they represent the legal challenges to their audiences. Like the litigation itself, each of these documentaries is built upon representational strategies that are intended to have the maximum impact on their audiences. Tying the Knot and The End of Second Class replicate the legal arguments and litigation strategies used by advocates of same-sex marriage. In particular, I analyse how each film represents the case for same-sex marriage through an appeal to three markers of equality rights discourses: rights evolve over time; rights are comparative; rights are indicators of national belonging. I contend that in their reliance on these markers, Tying the Knot and The End of Second Class unwittingly re-inscribe dominant notions of what it means to have full and equal national belonging and, thus, delimit what it means to be a “good” sexual citizen. Resume: Cet article explore comment les arguments juridiques en faveur de la reconnaissance des mariages entre personnes de meme sexe, aux Etats-Unis et au Canada, sont representes dans deux documentaires recents: Tying the Knot: The Union That’s Dividing America (Etats-Unis, 2004) et The End of Second Class (Canada, 2006). Je m’interesse notamment aux manieres dont ces films presentent les contestations judiciaires a leurs auditoires. Comme les litiges, ces documentaires sont construits sur des strategies representationnelles qui ont pour but d’avoir un impact maximal sur leurs auditoires. Ainsi, Tying the Knot et The End of Second Class reproduisent les arguments juridiques et les strategies de litige utilises par les defenseurs des mariages entre personnes de meme sexe. J’analyse, plus particulierement, comment les deux films presentent ces proces a l’aide de trois themes recurrents : (1) les droits evoluent avec le temps; (2) les droits sont comparatifs; (3) les droits representent des indicateurs d’une appartenance nationale. Je soutiens qu’en fonction de ces idees, Tying the Knot et The End of Second Class reintroduisent inconsciemment certaines notions dominantes de ce que signifie avoir une appartenance nationale pleine et egale et, par consequent, delimitent ce que veut dire etre un « bon » citoyen sexuel.

Here Kallestrup presents a succinct introduction to some of the latest thinking about the notorious mind-body problem.

The film From a Classical Position (1997) is a fully collaborative work between a notable dancer and performer and a notable choreographer, being danced, directed, and edited by Dana Caspersen and William Forsythe of the late Ballett Frankfurt. By looking closely at the film, its origins, and its process of creation, we gain an understanding of Caspersen and Forsythe's way of collaborating and their interest in working with other media and formats. Uncompromising if not difficult for a general dance audience, it is also somewhat didactic and offers insights into some of the Ballett Frankfurt's methods of generating movement, choreographic structures, and the importance of classical technique to a distinctive movement vocabulary:[The film] was also a little message to the British, who I'm sure were curious about us. It was a little missile to them, saying yes we are the Frankfurt Ballet, yes we perform before so many seats in the Opera House. We are the same people and this is what we do … There is the obvious classical training and this is how we are dealing with it. (Forsythe 1999)

Orr argues that the latest attack on evolution is cleverly argued, biologically informed — and wrong. This is his review of Behe's book, Darwin's Black Box: The Biochemical Challenge to Evolution.‘Just don't pull the knot tight before being certain that you have got hold of the right end.’ Wittgenstein.

In 1926 and 1927, James W. Alexander and Kurt Reidemeister claimed to have made “the same” crucial breakthrough in a branch of modern topology which soon thereafter was called knot theory. A detailed comparison of the techniques and objects studied in these two roughly simultaneous episodes of mathematical research shows, however, that the two mathematicians worked in quite different mathematical traditions and that they drew on related, but distinctly different epistemic resources. These traditions and resources were local, not universal elements of mathematical culture. Even certain common features of the main publications such as their modernist, formal style of exposition can be explained by reference to particular constellations in the intellectual and professional environments of Alexander and Reidemeister. In order to analyze the role of such elements and constellations of mathematical research practice, a historiographical perspective is developed which emphasizes parallels with the recent historiography of experiment. In particular, a notion characterizing those “working units of scientific knowledge production” which Hans-Jörg Rheinberger has termed “experimental systems” in the case of empirical sciences proves helpful in understanding research episodes such as those bringing about modern knot theory.

A harmonic morphism defined on $\mathbb{R}^3$ with values in a Riemann surface is characterized in terms of a complex analytic curve in the complex surface of straight lines. We show how, to a certain family of complex curves, the singular set of the corresponding harmonic morphism has an isolated component consisting of a continuously embedded knot.AMS 2000 Mathematics subject classification: Primary 57M25. Secondary 57M12; 58E20

In 1996, Cromwell and Nutt conjectured that α(L) − c (L) = 2 for a link L if and only if L is alternating. In this paper we calculate that α(L) = c (L) for some non-alternating pretzel links L, define a new invariant ρ(L) of adequate links L and show that for each non-negative integer n, there is a prime adequate knot K such that α(K) − c (K) = −2n. We conjecture that α(L) − c (L) = 2ρ(L) for any adequate link L.

We construct a family of hyperbolic 3-manifolds whose fundamental groups admit a cyclic presentation. We prove that all these manifolds are cyclic branched coverings of S3 over the knot 52 and we compute their homology groups. Moreover, we show that thecyclic presentations correspond to spines of the manifolds.

A variety of legal problems exist with the UN weapons inspection régime applicable to Iraq. These problems hinder the assurance that Iraq can be disarmed of the ability to produce biological or chemical weapons. Given this fact, the stalemate produced by the mid-December 1998 air strikes against that country might be best resolved by a reconfigured inspection program which aims at addressing Iraqi weapons of mass destruction efforts in the context of global security policy regarding such weaponry, with due account taken of the desires of Iraq's neighbors and the importance of reintegrating that nation into the world community.

We find presentations for the groups of Cappell-Shaneson 2-knots and other solvable 2-knot groups which are optimal in terms of deficiency and number of generators.

This paper compares the definitions of finite-type invariants due to Ohtsuki and to Garoufalidis, showing that, residually, type 3m of the former equals type m of the latter. It also shows that type 2m Ohtsuki invariants define knot invariants of type 3m (first proved by Habegger)., Comment: 13 pages, Postscript

In this paper, we study periodic braid representations of periodic links. It is shown that no 2-bridge non-fibred knot has a periodic braid representation and conditions under which periodic links are fibred are given. We give a construction of all periodic links over a fixed factor link.

A quandle is the algebraic distillation of the second and third Reidemeister moves, on unframed links. Quandles have been studied by many people including Kauffman[K], Fenn and Rourke[F-R] and Joyce [J]. Joyce defines the fundamental quandle, which is a classifying invariant of irreducible, unframed links. Fenn and Rourke, who study generalised quandles or racks in [F—R], show that the natural map from the fundamental quandle of a knot K to the knot group is never injective if K is a connected sum. We now prove that the natural map from the fundamental quandle to the fundamental group of the complement of a link in S3 is injective if and only if the link is prime.

In this paper we consider Dehn surgery and essential annuli whose two boundary components are in distinct components of the boundary of a 3-manifold.Let Nl be an orientable 3-manifold with boundary, Kl a knot in Nl, and N2 the 3-manifold obtained by performing γ-Dehn surgery Kl. In detail, let Vl be a regular neighbourhood Kl, X = Nl − int Vl the exterior of Kl, T the toral component ∂Vl of ∂X, and γ a slope on T. Then we obtain the 3-manifold N2 by attaching a solid torus V2 to X so that γ bounds a disc in V2. Let K2 be the core of V2. Let π be the slope of a meridian loop of Kl, and Δ the distance between the slopes π and γ, i.e. the minimal number of intersection points of the two slopes on T. Suppose for i = 1 and 2 that Ni contains a proper annulus Ai such that the two components of ∂Ai are essential loops on distinct incompressible components of ∂Ni. Then note that Ai is essential, i.e. incompressible and ∂-incompressible in Ni.

Kontsevich’s integral is a knot invariant which contains in itself all knot invariants of finite type, or Vassiliev’s invariants. The value of this integral lies in an algebra A0, spanned by chord diagrams, subject to relations corresponding to the flatness of the Knizhnik-Zamolodchikov equation, or the so called infinitesimal pure braid relations [11].

Projecting a knot onto a plane – or, equivalently, looking at it through one eye – one sees a more or less complicated plane curve with a number of crossings (‘nodes’); viewing it from certain positions, some other more complicated singularities appear. If one spends a little time experimenting, looking at the knot from different points of view, then provided the knot is generic, one can convince oneself that there is only a rather short list of essentially distinct local pictures (singularities) – see Fig. 3 below. All singularities other than nodes are unstable: by moving one's eye slightly, one can make them break up into nodes. For each type X the following two numbers can easily be determined experimentally:1. the codimension in ℝ3 of the set View(X) of centres of projection (viewpoints) for which a singularity of type X appears, and2. the maximum number of nodes n into which the singularity X splits when the centre of projection is moved.

In this paper we develop a method which may be used to compute the Chern—Simons invariants of a large class of representations on a large class of manifolds. This class includes all representations on all Seifert fiber spaces, all graph manifolds, and some hyperbolic manifolds. I owe many thanks to Peter Scott, John Harer, Frank Raymond, Ron Fintushel, Paul Kirk and Eric Klassen, without whose help and support this paper could not have been written. After covering some background material, we will compute the Chern—Simons invariants of all Seifert fiber spaces. The techniques we use are very natural for Seifert fiber spaces, but work equally well for many other manifolds after the techniques are translated into the language of surgery. We finish by translating the techniques into a sequence of moves which may be used to compute Chern—Simons invariants in a way similar to that in which skein relations may be used to compute knot invariants. First, we will define the Chern-Simons invariant and list some related facts and definitions. Throughout the paper we will use the group of unit quaternions, denoted by Sp r Geometrically, Spj is a 3-sphere with +1 at the north pole and — 1 at the south pole. Two elements of Spj commute if and only if they lie on a great circle running through +1 . The conjugacy classes are 2-spheres perpendicular to this family of great circles, and every element can be expressed as the commutator of two elements. The Chern-Simons invariant is defined for connections on the trivial Spx bundle over a 3-manifold. Let w be a connection on the trivial Spj bundle over a closed 3manifold. Definition. The Chern-Simons invariant of w is

In 1988, E. Witten proposed an array of invariants (quantumG-invariants) for a 3-manifold associated with a compact simple Lie groupGbased on the quantum field theory [22]. N. Reshetikhin and V. Turaev [20] gave a mathematical approach to these invariants forG=SU(2) by using representations of the quantum groupUq(sl(2, ℂ)). See also [2, 11, 12, 14, 15, 16] for other approaches to these invariants: [16] may be the simplest way (for knot theorists) to understand the existence of these invariants.

Every knot admits a special projection with the property that under the projection discs in the canonical Seifert surface project disjointly. Under an isotopy, such a projection can be turned into a connected sum of what we call inseparable projections. The main result is that if there is no band in an inseparable projection with half-twisting number +1 or −1, then the projection is not a projection of the trivial knot. To prove this a non-cyclic Coxeter group is constructed as a quotient of the knot group. The construction is possibly of interest in itself. The techniques developed are applied to give a criterion to decide when an inseparable projection with 3 discs comes from the trivial knot.

LetL⊂S3be a knot or a link. A tunnel system forLis a collection of disjoint arcst1, …tsproperly embedded inS3−N(L) so thatis a handlebody. Alternatively one can view thet1, …tsascocores of 2-handles which have to be attached to a handlebody in order to obtainS3−N(L). It follows immediately that this handlebody is of genuss+1. Thetunnel numberofL, denoted byt(L), is defined to be the minimal cardinality of all such collections.

We show that a PD3-complex P such that π = π1(P) is infinite and has a non-trivial finite normal subgroup must be homotopy equivalent to RP2 × S1. Hence if A is an abelian normal subgroup of a 2-knot group πK which is not contained in the commutator subgroup πK′ and πK′ is infinite then A is torsion free.

Examples of hyperbolic knots in S3 are given such that their complements contain quasi-Fuchsian non-Fuchsian surfaces. In particular, this proves that there are hyperbolic knots that are not toroidally alternating.

The importance of this result lies primarily in the fact [HLM] that the figure eight knot is universal. That is, that all closed, orientable 3-manifolds are obtainable as branched covers over S, branched over the knot. We also obtain results about incompressible (embedded) tori in some cases. Existence or nonexistence of injectively immersed tori is critical to the understanding of a 3-manifold in light of the Jaco-Shalen and Johannson torus decomposition [J-S,Jh] which plays such a pivotal role in Thurston’s geometrization conjecture and the recent result of Gabai and Casson (independently, see [Ga]) which, when combined with earlier results of Mess and Scott (see [M],[Sc]) shows that a 3-manifold which admits an injectively immersed torus, but no incompressible surfaces, must be Seifertfibered. Our approach to developing this algorithm will be partly geometric and partly combinatorial in nature. We will first describe a fixed geometric structure on S which lifts in a particularly nice way to a geometric structure on any branched cover of S, branched over the figure eight knot, which has the required minimum branching index. We will then use this geometric structure to gradually reduce the problem of finding injectively immersed tori in this branched cover to a problem of finding paths in a certain graph which satisfy certain easily verified conditions. We will also obtain an a priori upper bound on the length of paths which must be considered, so that our algorithm can not only find tori when they exist, but also ascertain when they do not. The overall organization of this paper is as follows: the geometric structures that we will need (Euclidean cone manifold structures) are described in Section 1. Section 2 discusses the particular cone manifold structure on S which will be lifted to the branched covers of S. Section 3 describes the first dimensional reduction that we will need, reducing questions about tori in 3-manifolds to questions about geodesics in 2-manifolds. Section 4 describes how to make the actual calculations needed in section 3 from combinatorial data

SUMMARYA method is presented to perform path planning in the Cartesian space. The motion velocity and acceleration are continuous. This is the first polynomial path planning algorithm in the Cartesian space working in real-time; it does not need an advanced knowledge of the trajectory and can be used when knot points are provided on-line by a sensor. The Bézier representation is used to compute a fifth degree polynomial path. It has been tested on an industrial robot controller.

In this paper we show that the cobordism classes of theta curves in S3 form a group under vertex connected sum. We investigate this group by means of knot cobordism and link cobordism.

Through the work of Julia Kristeva, this paper challenges Freud's laws that everyone is always already gendered, that the mother is feminine and every infant masculine, and that one cannot love the same (gender). The figure of the Madonna, seen through the paintings of Giovanni Bellini, is used to theorize the time in the life of a child before Oedipus and to undo the conceptual knot with which Freud has bound the feminine to the maternal.

An important problem in the topology of 3-manifolds is to classify manifolds obtained by Dehn surgeries on a knot in a closed 3-manifold, or equivalently, Dehn fillings of a 3-manifold M with boundary a torus.

Let be an oriented knot in S3 and a solid torus endowed with a preferred framing which contains in its interior. By ρ and λ we denote the wrapping and winding numbers of in respectively. That is, they are the geometric and algebraic intersection numbers of and a meridian disk of . For an integer μ, let τμ be an orientation-preserving homeomorphism of satisfying τμ(m) = m and τμ(l) = l + μm in H1(∂), where (m, l) is a meridian-longitude pair of . We call τμ(), denoted by μ, the knot obtained from by μ-twisting along .

A longstanding open question in low dimensional topology was raised by J. H. C. Whitehead in 1941 [9]: “Is any subcomplex of an aspherical, two-dimensional complex itself aspherical?” The asphericity of classical knot complements [7] provides evidence that the answer to Whitehead's question might be “yes”. Indeed, each classical knot complement has the homotopy type of a two-complex which can be embedded in a finite contractible two-complex. This property is shared by a large class of four-manifolds; these are the ribbon disc complements, whose asphericity has been conjectured, and even claimed, but never proven. (See [4] for a discussion.) It is reasonable and convenient to formulate the following.

In this paper we investigate totally geodesic surfaces in hyperbolic 3-manifolds. In particular we show that if M is a compact arithmetic hyperbolic 3-manifold containing an immersion of a totally geodesic surface then it contains infinitely many commensurability classes of such surfaces. In addition we show for these M that the Chern-Simons invariant is rational.We also show, that unlike the figure-eight knot complement in S3, many knot complements in S3 do not contain an immersion of a closed totally geodesic surface.

Let F be a closed connected and non-orientable surface smoothly embedded in the 4-sphere S4 with normal Euler number e(F) = 0. We note that if e(F) = 0, then the non-orientable genus n is even (ef. [7]) and the tubular neighbourhood N(F) of F in S4 which is a D2-bundle over F has a trivial I-subbundle. Let τ be a trivial I-subbundle of N(F) and let τ* = F × I ⊂ N(F) be its orthogonal I-subbundle which is twisted. Then is a closed connected genus n – 1 orientable surface smoothly embedded in S4 and doubly covers F. We call this surface a doubled surface of F in S4 (associated with τ). If a trivial I-subbundle τ is given, then we see that the knot type of F* ⊂ S4 is uniquely determined.

Let K be an oriented knot in the 3-sphere S3. An exterior of K is the closure of the complement of a regular neighbourhood of K, and is denoted by E(K). A Seifert surface for K is an oriented surface S( ⊂ S3) without closed components such that ∂S = K. We denote S ∩ E(K) by Ŝ, and we regard S as obtained from Ŝ by a radial extension. S is incompressible if Ŝ is incompressible in E(K). A tunnel for K is an embedded arc τ in S3 such that τ ∪ K = ∂τ. We denote τ ∪ E(K) by τ, and we regard τ as obtained from τ by a radial extension. Let τ1, τ2 be tunnels for K. We say that τ1 and τ2 are homeomorphic if there is a self-homeomorphism f of E(K) such that f(τ1) = τ2. The tunnels τ1 and τ2 are isotopic if τ1 is ambient isotopic to τ2 in E(K). Then the main result of this paper is as follows: Theorem. Let K be a knot in S3, and let τ1, τ2 be tunnels for K. Suppose that there are incompressible Seifert surfaces S1 S2 for K such that S1 ∪ S2 = K, and τi ⊂ Si (i = 1, 2). If τ1 and τ2 are isotopic, then there is an ambient isotopyhτ (0 ≤ t ≤ 1) of S3 such that ht(K) = K, and h1(τ1) = τ2.