-dimensional Euclidean manifolds represented by locally regular coloured graphs
3-manifold spines and bijoins.
We describe a combinatorial algorithm for constructing all orientable 3-manifolds with a given standard bidimensional spine by making use of the idea of bijoin (Bandieri and Gagliardi (1982), Graselli (1985)) over a suitable pseudosimplicial triangulation of the spine.
3-Manifolds which are unions of three solid tori.
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.