The Morse–Bott inequalities, orientations, and the Thom isomorphism in Morse homology

Thomas Olaf Rot

doi:10.1016/j.crma.2016.08.003

The Morse–Bott inequalities, orientations, and the Thom isomorphism in Morse homology

Thomas Olaf Rot

Mathematics

Research output: Contribution to Journal › Article › Academic › peer-review

Abstract

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.

Original language	English
Pages (from-to)	1026-2028
Number of pages	2
Journal	Comptes rendus de l'Académie des Sciences. Série I, Mathématique
Volume	354
Issue number	10
DOIs	https://doi.org/10.1016/j.crma.2016.08.003
Publication status	Published - 1 Oct 2016

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The Morse–Bott inequalities, orientations, and the Thom isomorphism in Morse homology

Abstract

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