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

2016/07/21 by Thomas O. Rot, Rot, Thomas O.
Mathematics · #55N35 #58A99 #58E05 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Symplectic Geometry (math.SG) #math.AT #math.GT #math.SG #msc:55N35 #msc:58A99 #msc:58E05

paper · pdf · doi:10.48550/arxiv.1607.06244

arxiv created 2016/07/21 · arxiv updated 2016/07/22

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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