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We exhibit some (compact and cusped) finite-volume hyperbolic 4-manifolds M with perfect circle-valued Morse functions, that is circle-valued Morse functions f\colon M \to S^1 with only index 2 critical points. We construct in particular one example where every generic circle-valued function is homotopic to a perfect one. An immediate consequence is the existence of infinitely many finite-volume (compact and cusped) hyperbolic 4-manifolds M having a handle decomposition with bounded numbers of 1- and 3-handles, so with bounded Betti numbers b_1(M), b_3(M) and rank \mathrm {rk}(\pi _1(M)). [ABSTRACT FROM AUTHOR]

Within the poetic digital space of Virtual Reality philosophical and cultural narratives collide. Do artistic experiments in VR provide the ultimate freedom for our development as a species or plunge it into passive reception of pure violence ? This article aims to chart a path through a small slice of thought and affective experiences of VR on the basis of a practical application of phenomenological reflection and the somatic movement practice Skinner Releasing Technique (SRT). The practical experiences of VR to be discussed are based on one particular VR artwork: MAN A VR by Gibson / Martelli. Affect, by way of phenomenology, bridges virtual reality and embodied lived experience. The result is an expansion of the somatic register of VR. [ABSTRACT FROM AUTHOR]

We exhibit a finite set of local moves that connect any two surgery presentations of the same 3-manifold via framed links in S3. The moves are handle-slides and blowdowns/ ups of a particular simple kind. [ABSTRACT FROM AUTHOR]

Let the Δ-complexity σ(M) of a closed manifold M be the minimal number of simplices in a triangulation of M. Such a quantity is clearly submultiplicative with respect to finite coverings, and by taking the infimum on all finite coverings of M normalized by the covering degree, we can promote σ to a multiplicative invariant, a characteristic number already considered by Milnor and Thurston, which we denote by σ∞(M) and call the stable Δ-complexity of M.We study here the relation between the stable Δ-complexity σ∞(M) of M and Gromov's simplicial volume ||M||. It is immediate to show that ||M|| ≤ σ∞ (M) and it is natural to ask whether the two quantities coincide on aspherical manifolds with residually finite fundamental groups. We show that this is not always the case: there is a constant Cn < 1 such that ||M|| ≤ Cnσ∞(M) for any hyperbolic manifold M of dimension n ≥ 4.The question in dimension 3 is still open in general. We prove that σ∞(M) = ||M|| for any aspherical irreducible 3-manifold M whose JSJ decomposition consists of Seifert pieces and/or hyperbolic pieces commensurable with the figure-eight knot complement. The equality holds for all closed hyperbolic 3-manifolds if a particular three-dimensional version of the Ehrenpreis conjecture is true. [ABSTRACT FROM AUTHOR]

We prove that a closed smooth 4-manifold has shadow-complexity zero if and only if it is a kind of four-dimensional graph manifold, which decomposes into some particular blocks along embedded copies of S2 × S1, plus some complex projective spaces. We deduce a classification of all smooth 4-manifolds with finite fundamental group and shadow-complexity zero. [ABSTRACT FROM PUBLISHER]

We show that only finitely many links in a closed 3-manifold can have homeomorphic complements, up to twists along discs and annuli. Using the same techniques, we prove that by adding 2-handles on the same link we get only finitely many smooth cobordisms between two given closed 3-manifolds. As a consequence, there are only finitely many closed smooth 4-manifolds constructed from some Kirby diagram with bounded number of crossings, discs, and strands, or from some Turaev special shadow with bounded number of vertices. (These are the 4-dimensional analogues of Heegaard diagrams and special spines for 3-manifolds.) We therefore get two filtrations on the set of all closed smooth orientable 4-manifolds with finite sets. The two filtrations are equivalent after linear rescalings, and their cardinality grows at least as nc · n. [ABSTRACT FROM AUTHOR]