A proof of Morse's theorem about the cancellation of critical points

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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Additional Info

Field Value
Source Comptes Rendus de l'Académie des Sciences - Series I - Mathematics
Author Laudenbach, Francois
Maintainer CCSD
Last Updated May 10, 2026, 10:09 (UTC)
Created May 10, 2026, 10:09 (UTC)
Identifier hal-00842792
Language en
Rights https://about.hal.science/hal-authorisation-v1/
contributor Laboratoire de Mathématiques Jean Leray (LMJL) ; Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST) ; Université de Nantes (UN)-Université de Nantes (UN)-Centre National de la Recherche Scientifique (CNRS)
creator Laudenbach, Francois
date 2013-06-10T00:00:00
harvest_object_id c0b616e5-0e3a-43c5-86e9-169df5555a37
harvest_source_id 3374d638-d20b-4672-ba96-a23232d55657
harvest_source_title test moissonnage SELUNE
metadata_modified 2026-04-17T00:00:00
relation info:eu-repo/semantics/altIdentifier/arxiv/1307.2545
set_spec type:ART