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This is a pseudo-historical survey about some aspects of lens spaces and their relations with cyclic quotient singularities. References are ordered by the year of publication. Their list is not exhaustive.

International audience

The extant letters exchanged between Kervaire and Milnor during their collaboration from 1958–1961 concerned their work on the classification of exotic spheres, culminating in their 1963 Annals of Mathematics paper. Michel Kervaire died in 2007; for an account of his life, see the obituary by Shalom Eliahou, Pierre de la Harpe, Jean-Claude Hausmann, and Claude Weber in the September 2008 issue of the Notices of the American Mathematical Society. The letters were made public at the 2009 Kervaire Memorial Conference in Geneva. Their publication in this issue of the Bulletin of the American Mathematical Society is preceded by our commentary on these letters, providing some historical background.

Let(formula here)be the germ of a finite (that is, proper with finite fibres) complex analytic morphism from a complex analytic normal surface onto an open neighbourhood U of the origin 0 in the complex plane C2. Let u and v be coordinates of C2 defined on U. We shall call the triple (π, u, v) the initial data.Let Δ stand for the discriminant locus of the germ π, that is, the image by π of the critical locus Γ of π.Let (Δα)α∈A be the branches of the discriminant locus Δ at O which are not the coordinate axes.For each α ∈ A, we define a rational number dα by(formula here)where I(–, –) denotes the intersection number at 0 of complex analytic curves in C2. The set of rational numbers dα, for α ∈ A, is a finite subset D of the set of rational numbers Q. We shall call D the set of discriminantal ratios of the initial data (π, u, v). The interesting situation is when one of the two coordinates (u, v) is tangent to some branch of Δ, otherwise D = {1}. The definition of D depends not only on the choice of the two coordinates, but also on their ordering.In this paper we prove that the set D is a topological invariant of the initial data (π, u, v) (in a sense that we shall define below) and we give several ways to compute it. These results are first steps in the understanding of the geometry of the discriminant locus. We shall also see the relation with the geometry of the critical locus.

International audience

In this paper we are interested in symmetries of alternating knots, more precisely in those related to achirality. We call the following statement Tait's Conjecture on alternating achiral knots: Let K be an alternating achiral knot. Then there exists a minimal projectionof K in S 2 � S 3 and an involution ' : S 3 ! S 3 such that: 1) ' reverses the orientation of S 3 ; 2) '(S 2 ) = S 2 ; 3) '(�) = �; 4) ' has two fixed points onand hence reverses the orientation of K. The purpose of this paper is to prove this statement. For the historical background of the conjecture in Peter Tait's and Mary Haseman's papers see (15).

This article reports on the current status of the system of the French military reserve. By reviewing a brief history of France’s military, the author shows the existing ambivalence regarding the establishment of a permanent part-time force. In France, conscription was suspended in 1996, and a smaller professional military was created. This smaller force required a review of the needs and role of the French reserve force. Today, in France there are two reserve types: the operational and the ‘‘citizen’’ reserves. Each is examined in terms of its activities and the role, profiles, and motivations of its members. This analysis sheds light on the initial question of whether the French reserve is a real or an abstract force. The French military reserve plays not just a symbolic but also a purposive role, although essentially limited to the national territory.

In this essay, we present our interpretation of the work of P. Tait and M. Haseman on achiral alternating knots. We have tried to elucidate the meaning of several concepts used by them such as: Amphicheirals, skew-amphicheirals, 1st or 2nd order, 1st or 2nd class, distorsions, etc. We also comment on some of their many pictures.

Let $L$ be an unsplittable, prime, oriented, alternating link type in $S^3$ . Let $D$ be a reduced alternating diagram representing $L$ . We define the Murasugi atoms of $D$ as the oriented link types represented by the prime factors of the Murasugi special components of $D$ . We prove (an invariance theorem) that the collection of Murasugi atoms depends only on $L$ and not on $D$ . This has the following corollary. Let $L$ be as above and assume that $L$ is achiral. Write its HOMFLY polynomial as $P_{L}(v,z)\,{=}\,\sum_{m}^{M} b_{j}(v) z^j$ . Then $b_{M}(v)\,{=}{\pm}\, \beta(v) \beta(v^{-1})$ for some polynomial $\beta(v) \in\mathbb{Z}[v, v^{-1}]$ . As a consequence, the leading coefficient of the Conway polynomial of $L$ is a square (up to sign).

L’article aborde un ouvrage et un texte majeurs de Pierre Clastres, Archeologie de la violence et « Malheur du guerrier sauvage », et reconnait l’auteur comme l’ethnologue francais precurseur dans le domaine des recherches relatives aux phenomenes de violence au sein des societes dites primitives. S’appuyant sur ses experiences de terrain parmi les Amerindiens, P. Clastres montre en effet de quelle maniere les theories emises par la communaute scientifique ne sont pas aptes a expliquer les origines et les raisons d’etre des processus de violence. Il nous livre ainsi sa propre theorie du besoin de guerre de ces societes comme principal moyen de conserver leur unite, d’eviter toute division interne et de maintenir leur autonomie, leur independance territoriale et economique. Apres avoir demontre le role central de la violence comme moteur de la vie sociale et par consequent comme etant au cœur de tout etre social, P. Clastres s’attache au corps des guerriers. Il aborde le profil des guerriers, leur role, l’organisation egalitaire du corps et l’absence de discipline, les modes de controle de ce groupe detenant la force, la maniere d’eviter le pouvoir de ce collectif et l’alienation de chacun des membres a la societe, le devenir certain du guerrier et sa proximite avec la mort.

Duas populações alopátridas de cascudos, ambas provisoriamente denominadas Hypostomus margaritifer (Regan, 1907) (Osteichthyes, Loricariidae), foram coletadas no reservatório de Corumbá, Estado de Goiás e no reservatório de Itaipu, Estado do Paraná. Diferenças no padrão de coloração, presença ou ausência de placas abdominais e no tamanho máximo dos exemplares foram observadas entre estas populações. O status taxonômico dessas populações foi investigado através de duas técnicas diferentes: análise morfológica e de aloenzimas. A análise morfométrica não permitiu detectar diferenças expressivas entre as populações. Uma única diferença significativa nas freqüências alélicas foi encontrada no loco sAat-A, entretanto a conspecificidade é comprovada pelo alto valor de identidade genética (0,988). Uma descrição complementar de H. margaritifer é dada, assim como uma discussão dos trabalhos mais importantesTwo allopatrid populations of armoured catfishes, both referred to as Hypostomus margaritifer (Regan, 1907) (Osteichthyes, Loricariidae), were collected in the Corumbá reservoir (State of Goiás) and in the Itaipu reservoir (State of Paraná), Brazil. Differences in colour pattern, arrangement of abdominal platelets and maximum length of specimens were observed between these populations. Their taxonomic status was investigated through two different approaches: morphological and allozyme analysis. Morphometrics showed no expressive differences between these two populations and the holotype of H. margaritifer. A unique difference in allelic frequencies was observed in the sAat-A locus; nevertheless conspecificity of the two populations was confirmed by a high identity value (0.988). A complementary description of H. margaritifer is given as well as a discussion of the most important studies

Hypostomus fonchii sp. n. is described. Diagnostic characters are the unicuspid premaxillary and dentary teeth, present in subadults as well as in adults, and the elongated and broad tooth crown. Because these tooth characters are intermediate between Hypostomus and Cochliodon, and because dentition traits are the only characters diagnosing Cochliodon, the discovery of H. fonchii provides evidences for questioning the generic status of Cochliodon. We conclude that Cochliodon is a subjective junior synonym of Hypostomus. This work is the first part of our joint investigations on Hypostomus based on both morphological and molecular characters.

A travers l’approche et l’etude de l’ensemble des campagnes audiovisuelles de l’armee de Terre, l’auteur aborde la raison d’etre des productions televisuelles adressees au grand public et les difficultes de positionnement des responsables de la communication en fonction des contextes et des besoins de l’armee de Terre. Le propos illustre les exigences et les contraintes relatives a la conduite du changement au sein des armees, la professionnalisation actuelle des effectifs constituant le parfait exemple des processus innovants.

La presente contribution s’interesse au comportement de l’humain dans l’espace numerique. En depit de la democratisation des sensi­bilisations, il semblerait en effet que l’hygiene informatique reclamee pour chacun ne soit pas toujours respectee. En partant de constats precis produits a partir d’experimentations menees (campagne de phishing) aupres de popula­tions militaires, les auteurs cherchent a comprendre les raisons susceptibles d’expliquer pourquoi l’utilisateur demeure le maillon faible de la chaine de cybersecurite. Le poids des cultures professionnelle et militaire semble Claire­ment pouvoir etre mobilise, incitant les contributeurs a appeler de leurs vœux des evolutions majeures en termes de sensibilisation et d’entrainement pour le large public et plus generalement a une veritable revolution culturelle pour federer l’adhesion de tous et ameliorer de fait la cyber resilience des SI.

Purpose – This chapter aims to describe and analyze practices and activities linked with the traditions – and their transmission between the cadets – in Saint-Cyr, the French military academy. Methodology/approach – The methodological approach was anthropological, consisting of immersion, observation, and interviews during the first three years of training of the future French army officers. Findings – Traditions in Saint-Cyr are an opportunity for cadets to be elected by their comrades in order to lead the class. This contribution focuses on these elected cadets’ characteristics and shows that having such a responsibility comes along with advantages and privileges, and, at the end, with a better grading. Originality/value of the paper – It is the first time that a researcher was allowed to follow all activities and study a class in Saint-Cyr during the three-year training period. This study provides a look inside the daily cadets’ life and shows that the traditions are not just an anecdotal aspect of cadets’ life, but perfectly witnesses all challenges, power positions, and stakes associated with them.

A new Hypostomus species is described from the rio Cuiabá, upper rio Paraguay basin, Mato Grosso State, Brazil. The new species is distinguished from all other Hypostomus species, with exception of young specimens of H. latifrons, by the presence of a wide dark transverse bars on laterals of body and fins; and conspicuous dark vermiculations on abdominal region. From H. latifrons it differs by having just one pre-dorsal plate surrounding supraoccipital bone and by the maintenance of the dark saddles in adults. Added to the other fish species recently described from the upper rio Paraguay basin, this work helps to highlight that the region still functions as a potential source of new species. Uma espécie nova de Hypostomus é descrita do rio Cuiabá, bacia do alto rio Paraguai, Estado do Mato Grosso, Brasil. A espécie nova é diagnosticada de todas as outras congêneres, com exceção de H. latifrons, pela presença de amplas barras escuras transversais nas laterais do corpo e nadadeiras, e pelas conspícuas vermiculações escuras na região abdominal. De H. latifrons ela difere por ter somente uma placa pré-dorsal margeando o osso supraoccipital e pela manutenção das barras escuras transversais nos adultos. Somada a outras espécies de peixes recentemente descritas na bacia do alto rio Paraguai, este trabalho demonstra que a região ainda funciona como uma fonte potencial de espécies novas.

Quelle que soit la nature du groupe, l’etude du fait culturel ne doit pas etre assimilee au folklore ou a un passe fige. L’analyse des evolutions relatives aux cultures militaires est indispensable a la comprehension non seulement de l’institution dans son ensemble, mais egalement de son inscription au sein de la societe en general. Les mutations et les reformes ont ete nombreuses ces dernieres decennies, et a l’heure des armees francaises entierement professionnalisees, il est plus que jamais important de cerner ce que l’on entend par cultures militaires et de quelles manieres ces dernieres dessinent des caracteristiques organisationnelles, specifient les personnes, et caracterisent les liens entre les armees et la societe parente.

Good working relationship between civilians and military has been one of the key priorities of French Politicians in the last decade. President Jacques Chirac has himself in a political speech in 1996 mentioned a professionalisation of the military corpus which has raised concerns of the future of French armed forces and led to the transformation of the relationship between the military and non-military sector. A good example of this cultural transformation could be noted in the creation of the so-called JAPD (Journee d’Appel a la Preparation de Defense) which is a one day event during which the French young population is given the opportunity to have an insight into the military environment.

L’identité militaire est diverse et variée, mais le sens commun attribue encore au militaire l’image du combattant viril. Les femmes militaires sont-elles alors des garçons manqués ? Notre terrain d’enquête est celui des Ecoles de Coëtquidan. Entretiens avec élèves et cadres, tels les moniteurs de sport, l’observation directe (séance d’Entraînement Physique, Militaire et Sportif ; rallye, etc.) et l’analyse de documents (programmation de l’EPMS) nous aident à dégager une corporéité type de l’élève officier des armes, ainsi que ses conséquences éventuelles sur l’identité des femmes élèves officiers et sur les relations intersexuées. Il en résulte que, malgré la prédominance de valeurs viriles (courage, force, etc.) transmises par l’EPMS, auxquelles elles adhèrent, les femmes élèves officiers, plus ou moins bien acceptées par leurs homologues masculins, n’en perdent pas pour autant leur féminité. Military identity is diverse and different, but the common sense still assigns the image of the “male warrior”. Do military women really look like boys? Our ground of investigation concerns the Schools of Coëtquidan. Interviews with cadets and managers, like sport monitors; direct observation (Physical, Military and Sport Training; rally, etc.) and analysis of documents (Programming of the PMST) help us to define a typical “corporéité” (body usage) of cadets and the eventual consequences on identity of female cadets and on the gendered relationships. It results from it that, despite the predominance of male values (valour, strength, etc.) transmitted by the PMST, to which they adhere, the female cadets, more or less appreciated by their male counterparts, keep their femininity.

High altitude with low oxygen pressure and subsequent low blood saturation is known to lead eventually to HACE (High Altitude Cerebral Edema) and HAPE (Hi.Alt.Pulmonary Edema) even in healthy well-trained alpinists. Asthma is usually well tolerated in higher altitudes but still might be refered to as a predisposal to HAPE unless treated. The author reports a case of a 45 y.o.male asthmatic of Caucasian origin followed up to 6962m (highest spot on American continent between ChileArgentina) with measurement of O2 saturation-B.P.-H.R-PEVPeak-Flow-.

We give the first (as far as we know) complete description of the boundary of the Milnor fiber for some non-isolated singular germs of surfaces in ${\bf C}^3$. We study irreducible (i.e. $gcd (m,k,l) = 1$) non-isolated (i.e. $1 \leq k < l$) Hirzebruch hypersurface singularities in ${\bf C}^3$ given by the equation $z^m - x^ky^l = 0$. We show that the boundary $L$ of the Milnor fiber is always a Seifert manifold and we give an explicit description of the Seifert structure. From it, we deduce that : 1) $L$ is never diffeomorphic to the boundary of the normalization. 2) $L$ is a lens space iff $m = 2$ and $k = 1$. 3) When $L$ is not a lens space, it is never orientation preserving diffeomorphic to the boundary of a normal surface singularity., 13 pages

The complete D-loop sequence was obtained from 23 Hypostomus and 12 other species belonging to eight genera, from which seven are closely related to Hypostomus. The phylogenetic analysis of these sequences indicates that the genus Hypostomus is polyphyletic due to the exclusion of H. emarginatus and H. squalinus from the main Hypostomus clade. Moreover, this main Hypostomus clade includes all Cochliodon species examined here, indicating that Cochliodon can be considered as a subjective junior synonym of Hypostomus. This conclusion is also supported by the placement of Hypostomus fonchii within the Cochliodon clade, implying that the synapomorphic characters diagnosing Cochliodon are unfounded. Based on these results, a new vision of Hypostomus is proposed. Furthermore, our results confirm the previously reported polyphyly of Ancistrinae and question the monophyletic status of Hemiancistrus.

The aim of this article is to present an elementary introduction to classical knot theory. The word classical means two things. First, it means the study of knots in the usual 3D space R 3 or S 3. It also designates knot theory before 1984. In section 1 we describe the basic facts: curves in 3D space, isotopies, knots, links and knot types. We then proceed to knot diagrams and braids. Finally we introduce the useful notion of tangle due to John Conway. In section 2 we present some important problems of knot theory: classification, chirality, search for and computation of invariants. In section 3 we give a brief description of some knot families: alternating knots, two-bridge knots, torus knots. Within each family, the classification problem is solved. In section 4 we indicate two ways to introduce some structure in knot types: via ideal knots and via the knot complement.

Let f : C 2 →C be a polynomial function. It is well known that there exists a finite set A⊂C such that the restriction of f to C2−f−1(A) is a differentiable fibration onto C−A. Following Broughton in (Proc. Symp. Pure Math. 40 (1983) 167) we call the smallest of such A's the set of atypical values of f and write it Af. Let F be a generic fiber of f. The main goal of this article is to describe the monodromy on H1(F,Z) around an atypical value a∈Af. For that purpose we define and study a monodromic filtration on the homology with coefficients in Z : 0⊂M −1 ⊂M 0 ⊂M 1 ⊂M 2 =H 1 (F,Z) . The term M−1 is added to allow for the boundary of F. We introduce a compact model L a for the smooth part of the reduced curve associated to the affine fiber f−1(a). One important result of this article is theorem (8.12) which shows how H 1 ( L a ,Z) gives (via the transfer homomorphism) a precise description of the invariant cycles in H1(F,Z).

Nous donnons une bonne projection pour l'entrelac associe a un divide de Norbert A'Campo, pour une classe de divides que nous appelons extravertis et qui generalise la notion de slalom divide.

On fait generalement remonter l’allemand philosophique, c’est-a-dire l’allemand en tant que langue de la philosophie, a l’epoque de la Fruhaufklarung. Christian Thomasius, en decidant un beau jour de Tannee 1687 de faire cours en allemand, passe pour avoir inaugure une nouvelle ere de la philosophie en Allemagne et l’on accorde la plupart du temps a Christian Wolff le merite d’avoir veritablement fonde le vocabulaire philosophique allemand dans sa serie de traites intitules Vernunfftige Gedancken ..., parus a partir de 1713.2 En realite, si Thomasius et Wolff ont contribue de maniere determinante a l’etablissement de l’allemand comme langue de l’enseignement philosophique, sinon comme langue de la philosophie tout court (dans leur pays), l’histoire de l’allemand philosophique remonte bien plus haut dans le temps -jusqu’a la langue des mystiques du XIVe et du XVe siecle ou a celle des Reformateurs du XVIe. Bien entendu, il ne s’agit pas la de philosophes au sens strict, mais ces auteurs ont tout de meme contribue par leurs ecrits allemands a forger une langue dans laquelle allait pouvoir s’exprimer un discours philosophique. Rudolph Eucken a montre au siecle dernier deja tout ce que la terminologie philosophique allemande devait a ces auteurs.3 D’autre part, et contrairement a ce que l’on pourrait penser, l’allemand est loin d’etre absent de l’enseignement philosophique dans les universites du XVIIe siecle. Certes la langue de la philosophie est le latin, mais ce dernier a bien peu de rapports avec l’ideal d’elegance d’un Valla ou d’un Muret.

We give a counterexample to the generalized Kawauchi conjecture on the Conway polynomial of achiral knots which asserts that the Conway polynomial C(z) of an achiral knot satisfies the splitting property C(z) = F(z)F(-z) for a polynomial F(z) with integer coefficients. We show that the Bonahon–Siebenmann decomposition of an achiral and alternating knot is reflected in the Conway polynomial. More explicitly, the generalized Kawauchi conjecture is true for quasi-arborescent knots and counterexamples in the class of alternating knots must be quasi-polyhedral.

Les figures heroiques a Saint-Cyr sont ici abordees a travers une double approche, a la fois historique et sociologique. Celle-ci etablit plusieurs constats : un deficit culturel dans les domaines politique et litteraire chez les eleves d’aujourd’hui ; une etroite imbrication des dimensions mythologique, traditionnelle et historique toujours difficiles a demeler ; le « rajeunissement » des modeles de chef militaire et, avant toute incarnation, une construction archetypale du heros saint-cyrien.

Quelle que soit la nature du groupe, l’etude du fait culturel ne doit pas etre assimilee au folklore ou a un passe fige. L’analyse des evolutions relatives aux cultures militaires est indispensable a la comprehension non seulement de l’institution dans son ensemble, mais egalement de son inscription au sein de la societe en general. Les mutations et les reformes ont ete nombreuses ces dernieres decennies, et a l’heure des armees francaises entierement professionnalisees, il est plus que jamais important de cerner ce que l’on entend par cultures militaires et de quelles manieres ces dernieres dessinent des caracteristiques organisationnelles, specifient les personnes, et caracterisent les liens entre les armees et la societe parente.