Comptes Rendus
no. 10
Topology/Differential topology
The Morse–Bott inequalities, orientations, and the Thom isomorphism in Morse homology

Presented by: Claire Voisin

Thomas O. Rot1
1 Universität zu Köln, Mathematisches Institut, Weyertal 86-90, 50931 Köln, Germany
Comptes Rendus. Mathématique, Volume 354 (2016) no. 10, pp. 1026-1028.

The Morse–Bott inequalities relate the topology of a closed manifold to the topology of the critical point set of a Morse–Bott function defined on it. The Morse–Bott inequalities are sometimes stated under incorrect orientation assumptions. We show that these assumptions are insufficient with an explicit counterexample and clarify the origin of the mistake.

Les inégalités de Morse–Bott relient la topologie d'une variété compacte sans bord à celle de l'ensemble des points critiques d'une fonction de Morse–Bott définie sur cette variété. Elles sont parfois énoncées sous des hypothèses d'orientation inexactes. Nous montrons que ces hypothèses sont insuffisantes grâce à un contre-exemple explicite et clarifions l'origine de cette erreur.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2016.08.003

Thomas O. Rot 1

1 Universität zu Köln, Mathematisches Institut, Weyertal 86-90, 50931 Köln, Germany 
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Thomas O. Rot. The Morse–Bott inequalities, orientations, and the Thom isomorphism in Morse homology. Comptes Rendus. Mathématique, Volume 354 (2016) no. 10, pp. 1026-1028. doi : 10.1016/j.crma.2016.08.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.08.003/

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