7,288 research outputs found
A proof of Reidemeister-Singer's theorem by Cerf's methods
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
A generalization of several classical invariants of links
We extend several classical invariants of links in the 3-sphere to links in
so-called quasi-cylinders. These invariants include the linking number, the
Seifert form, the Alexander module, the Alexander-Conway polynomial and the
Murasugi-Tristram-Levine signatures.Comment: 25 pages, 6 figure
- …