[Une preuve du théorème de Morse sur lʼélimination de points critiques]
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 sur une variété différentiable. Notre preuve consiste à réduire la question au cas facile dʼune fonction dʼune variable.
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.
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@article{CRMATH_2013__351_11-12_483_0,
author = {Laudenbach, Fran\c{c}ois},
title = {A proof of {Morse's} theorem about the cancellation of critical points},
journal = {Comptes Rendus. Math\'ematique},
pages = {483--488},
publisher = {Elsevier},
volume = {351},
number = {11-12},
year = {2013},
doi = {10.1016/j.crma.2013.06.009},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2013.06.009/}
}
TY - JOUR AU - Laudenbach, François TI - A proof of Morseʼs theorem about the cancellation of critical points JO - Comptes Rendus. Mathématique PY - 2013 SP - 483 EP - 488 VL - 351 IS - 11-12 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2013.06.009/ DO - 10.1016/j.crma.2013.06.009 LA - en ID - CRMATH_2013__351_11-12_483_0 ER -
%0 Journal Article %A Laudenbach, François %T A proof of Morseʼs theorem about the cancellation of critical points %J Comptes Rendus. Mathématique %D 2013 %P 483-488 %V 351 %N 11-12 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2013.06.009/ %R 10.1016/j.crma.2013.06.009 %G en %F CRMATH_2013__351_11-12_483_0
Laudenbach, François. A proof of Morseʼs theorem about the cancellation of critical points. Comptes Rendus. Mathématique, Tome 351 (2013) no. 11-12, pp. 483-488. doi : 10.1016/j.crma.2013.06.009. http://www.numdam.org/articles/10.1016/j.crma.2013.06.009/
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