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3-manifold spines and bijoins.

Luigi Grasselli (1990)

Revista Matemática de la Universidad Complutense de Madrid

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.

A conjecture on Khovanov's invariants

Stavros Garoufalidis (2004)

Fundamenta Mathematicae

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 gauge-field approach to 3- and 4-manifold invariants

Bogusław Broda (1997)

Banach Center Publications

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 proof of Reidemeister-Singer’s theorem by Cerf’s methods

François Laudenbach (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

Heegaard splittings and Heegaard diagrams of a closed 3-manifold M are translated into the language of Morse functions with Morse-Smale pseudo-gradients defined on M . 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 dim M > 2 . The main tool that we introduce is an elementary swallow tail lemma which could be useful elsewhere.

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