Morse-Bott homology

Banyaga, Augustin; Hurtubise, David

doi:10.1090/S0002-9947-10-05073-7

Morse-Bott homology
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by Augustin Banyaga and David E. Hurtubise

Trans. Amer. Math. Soc. 362 (2010), 3997-4043

DOI: https://doi.org/10.1090/S0002-9947-10-05073-7

Published electronically: March 23, 2010

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Abstract:

We give a new proof of the Morse Homology Theorem by constructing a chain complex associated to a Morse-Bott-Smale function that reduces to the Morse-Smale-Witten chain complex when the function is Morse-Smale and to the chain complex of smooth singular $N$-cube chains when the function is constant. We show that the homology of the chain complex is independent of the Morse-Bott-Smale function by using compactified moduli spaces of time dependent gradient flow lines to prove a Floer-type continuation theorem.

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Morse-Bott homology
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