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

Francois Laudenbach (1)

1 LMJL - Laboratoire de Mathématiques Jean Leray

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.

Mots clés: Morse theory; critical points; pseudo-gradient

Domaines: Topologie géométrique [math.GT]

Francois Laudenbach. A proof of Morse's theorem about the cancellation of critical points. Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 2013, 351, pp.483-488. ⟨hal-00842792⟩