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

François Laudenbach

Annales de la faculté des sciences de Toulouse Mathématiques (2014)

  • Volume: 23, Issue: 1, page 197-221
  • ISSN: 0240-2963

Abstract

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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.

How to cite

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Laudenbach, François. "A proof of Reidemeister-Singer’s theorem by Cerf’s methods." Annales de la faculté des sciences de Toulouse Mathématiques 23.1 (2014): 197-221. <http://eudml.org/doc/275349>.

@article{Laudenbach2014,
abstract = {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 $\dim M&gt;2$. The main tool that we introduce is an elementary swallow tail lemma which could be useful elsewhere.},
author = {Laudenbach, François},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {Heegaard splitting; Morse theory; Cerf theory; pseudo-gradient field; ordered functions},
language = {eng},
number = {1},
pages = {197-221},
publisher = {Université Paul Sabatier, Toulouse},
title = {A proof of Reidemeister-Singer’s theorem by Cerf’s methods},
url = {http://eudml.org/doc/275349},
volume = {23},
year = {2014},
}

TY - JOUR
AU - Laudenbach, François
TI - A proof of Reidemeister-Singer’s theorem by Cerf’s methods
JO - Annales de la faculté des sciences de Toulouse Mathématiques
PY - 2014
PB - Université Paul Sabatier, Toulouse
VL - 23
IS - 1
SP - 197
EP - 221
AB - 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 $\dim M&gt;2$. The main tool that we introduce is an elementary swallow tail lemma which could be useful elsewhere.
LA - eng
KW - Heegaard splitting; Morse theory; Cerf theory; pseudo-gradient field; ordered functions
UR - http://eudml.org/doc/275349
ER -

References

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