A complete description of normal surfaces for infinite series of 3-manifolds.
A conjecture on Khovanov's invariants
We formulate a conjectural formula for Khovanov's invariants of alternating knots in terms of the Jones polynomial and the signature of the knot.
A criterion for homeomorphism between closed Haken manifolds.
A decomposition into homeomorphic handlebodies with naturally equivalent involutions.
A filtration of the set of integral homological 3-spheres.
A finite graphic calculus for 3-manifolds.
A gauge-field approach to 3- and 4-manifold invariants
An approach to construction of topological invariants of the Reshetikhin-Turaev-Witten type of 3- and 4-dimensional manifolds in the framework of SU(2) Chern-Simons gauge theory and its hidden (quantum) gauge symmetry is presented.
A generalized bridge number for links in 3-manifolds.
A geometric invariant of discrete groups.
A locally connected non-movable continuum that fails to separate
A new invariant on hyperbolic Dehn surgery space.
A Note on 2-fold Branched Covering Spaces of S3.
A note on a 3-dimensional homogeneous space
A note on irreducible Heegaard diagrams.
A polyhedral 2-sphere which fails to be locally flat at just one point
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.
A rational noncommutative invariant of boundary links.
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 Splicing formula for Casson-Walker's invariant.