A proof of Reidemeister-Singer's theorem by Cerf's methods

Francois Laudenbach (1)

1 LMJL - Laboratoire de Mathématiques Jean Leray

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.

Mots clés: Morse theory; Cerf theory; pseudo-gradient; ordered functions

Domaines: Topologie géométrique [math.GT]

Francois Laudenbach. A proof of Reidemeister-Singer's theorem by Cerf's methods. Annales de la Faculté des Sciences de Toulouse. Mathématiques., 2014, XXIII (1), pp.197 - 221. ⟨hal-00911576⟩