The Morse-Bott inequalities, orientations, and the Thom isomorphism in Morse homology
classification
🧮 math.GT
math.ATmath.SG
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morse-bottinequalitiesassumptionstopologyclarifyclosedcounterexamplecritical
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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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