Pairs of Morse functions

Olivier Thom

Journal of Singularities
volume 16 (2016), 115-129

Received: 7 April 2017. Received in revised form: 21 June 2017.

DOI: 10.5427/jsing.2017.16e

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The goal of this paper is to classify pairs of Morse functions in general position modulo the action of different groups. In particular, we obtain the classification of generic pairs of Morse functions, with or without target diffeomorphisms, and that of quotients of Morse functions.

We will also present a lemma which gives a sufficient condition for two pairs of functions to be conjugated.

Author(s) information:

O. Thom
IRMAR, Université de Rennes 1
IRMAR 6625, Campus de Beaulieu
35042 Rennes Cedex, France