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

Thomas O. Rot

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arXiv · 1607.06244

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

Thomas O. Rot

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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.

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Thomas O. Rot. 2016-07-21. The Morse-Bott inequalities, orientations, and the Thom isomorphism in Morse homology. https://arxiv.org/abs/1607.06244

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