A new technique for the link slice problem.
A non-abelian Seiberg-Witten invariant for integral homology 3-spheres.
A non-𝒵-compactifiable polyhedron whose product with the Hilbert cube is 𝒵-compactifiable
We construct a locally compact 2-dimensional polyhedron X which does not admit a 𝒵-compactification, but which becomes 𝒵-compactifiable upon crossing with the Hilbert cube. This answers a long-standing question posed by Chapman and Siebenmann in 1976 and repeated in the 1976, 1979 and 1990 versions of Open Problems in Infinite-Dimensional Topology. Our solution corrects an error in the 1990 problem list.
A norm for the cohomology of 2-complexes.
A Note on 2-fold Branched Covering Spaces of S3.
A note on a 3-dimensional homogeneous space
A note on a multi-variable polynomial link invariant
A note on a recursive formula of the Arf-Kervaire invariant.
A Note on Hyperbolic 3-Manifolds of the Same Volume.
A note on irreducible Heegaard diagrams.
A Note on Link Complements and Arithmetic Groups.
A note on pseudo-Anosov maps with small growth rate.
A note on the existence of -equivelar polyhedral maps.
A note on the rank of self-dual polyhedra
A Note on the Rational Cuspidal Curves
In this short note we give an elementary combinatorial argument, showing that the conjecture of J. Fernández de Bobadilla, I. Luengo-Velasco, A. Melle-Hernández and A. Némethi [Proc. London Math. Soc. 92 (2006), 99-138, Conjecture 1] follows from Theorem 5.4 of Brodzik and Livingston [arXiv:1304.1062] in the case of rational cuspidal curves with two critical points.
A note on unlinking numbers of Montesinos links.
Let K (resp. L) be a Montesinos knot (resp. link) with at least four branches. Then we show the unknotting number (resp. unlinking number) of K (resp. L) is greater than 1.
A partial order in the knot table.
A polynomial invariant for unoriented knots and links.
A polynomial invariant of rational homology 3-spheres.
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.