Comptes Rendus
no. 11-12
Differential Topology
A proof of Morseʼs theorem about the cancellation of critical points

Presented by: the Editorial Board

François Laudenbach1
1 Laboratoire de mathématiques Jean Leray, UMR 6629 du CNRS, faculté des sciences et techniques, université de Nantes, 2, rue de la Houssinière, 44322 Nantes cedex 3, France
Comptes Rendus. Mathématique, Volume 351 (2013) no. 11-12, pp. 483-488.

In this Note, we give a proof of the famous theorem of M. Morse dealing with the cancellation of a pair of non-degenerate critical points of a smooth function. Our proof consists of a reduction to the one-dimensional case where the question becomes easy to answer.

Dans cette Note, nous présentons une preuve du célèbre théorème de M. Morse concernant lʼélimination dʼune paire de points critiques non dégénérés pour une fonction C∞ sur une variété différentiable. Notre preuve consiste à réduire la question au cas facile dʼune fonction dʼune variable.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2013.06.009

François Laudenbach 1

1 Laboratoire de mathématiques Jean Leray, UMR 6629 du CNRS, faculté des sciences et techniques, université de Nantes, 2, rue de la Houssinière, 44322 Nantes cedex 3, France 
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François Laudenbach. A proof of Morseʼs theorem about the cancellation of critical points. Comptes Rendus. Mathématique, Volume 351 (2013) no. 11-12, pp. 483-488. doi : 10.1016/j.crma.2013.06.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.06.009/

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