A positional characterization of the (n-1)-dimensional Sierpiński curve in (η ≠ 4)
A proof of Reidemeister-Singer’s theorem by Cerf’s methods
Heegaard splittings and Heegaard diagrams of a closed 3-manifold are translated into the language of Morse functions with Morse-Smale pseudo-gradients defined on . We make use in a very simple setting of techniques which Jean Cerf developed for solving a famous pseudo-isotopy problem. In passing, we show how to cancel the supernumerary local extrema in a generic path of functions when . The main tool that we introduce is an elementary swallow tail lemma which could be useful elsewhere.
A quick proof of the 4-dimensional stable surgery theorem.
A rational noncommutative invariant of boundary links.
A remark on the action of the mapping class group on the unit tangent bundle
We prove that the standard action of the mapping class group of a surface of sufficiently large genus on the unit tangent bundle is not homotopic to any smooth action.
A set of moves for Johansson representation of 3-manifolds
A Dehn sphere Σ in a closed 3-manifold M is a 2-sphere immersed in M with only double curve and triple point singularities. The Dehn sphere Σ fills M if it defines a cell decomposition of M. The inverse image in S² of the double curves of Σ is the Johansson diagram of Σ and if Σ fills M it is possible to reconstruct M from the diagram. A Johansson representation of M is the Johansson diagram of a filling Dehn sphere of M. Montesinos proved that every closed 3-manifold has a Johansson representation...
A short introduction to shadows of 4-manifolds
We give a self-contained introduction to the theory of shadows as a tool to study smooth 3-manifolds and 4-manifolds. The goal of the present paper is twofold: on the one hand, it is intended to be a shortcut to a basic use of the theory of shadows, on the other hand it gives a sketchy overview of some of the most recent results on shadows. No original result is proved here and most of the details of the proofs are left out.
A spectral sequence for orbifold cobordism
The aim of this paper is to introduce a spectral sequence that converges to the cobordism groups of orbifolds with given isotropy representations. In good cases the E¹-term of this spectral sequence is given by a certain cobordism group of orbibundles over purely ineffective orbifolds which can be identified with the bordism group of the classifying space of the Weyl group of a finite subgroup of O(n). We use this spectral sequence to calculate some cobordism groups of orbifolds for low dimensions,...
A Splicing formula for Casson-Walker's invariant.
A stable classification of Lefschetz fibrations.
A sufficient condition for a group of homeomorphisms to be affine.
A Surgery Sequence in Dimension Four; The Relations with Knot Concordance.
A three-dimensional spheroidal space which is not a sphere
A topological collapse number for all spaces
A unique factorization theorem for countable products of circles
A universal bound for surfaces in 3-manifolds with a given Heegaard genus.
A universal class of 4-colored graphs.
A vanishing theorem for twisted Alexander polynomials with applications to symplectic 4-manifolds
In this paper we show that given any 3-manifold and any non-fibered class in there exists a representation such that the corresponding twisted Alexander polynomial is zero. We obtain this result by extending earlier work of ours and by combining this with recent results of Agol and Wise on separability of 3-manifold groups. This result allows us to completely classify symplectic 4-manifolds with a free circle action, and to determine their symplectic cones.
A volume-preserving counterexample to the Seifert conjecture.
A wild Cantor set in with simply connected complement