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ISSN 1088-6850(e) ISSN 0002-9947(p)

Morse-Bott homology

Author(s): Augustin Banyaga; David E. Hurtubise
Journal: Trans. Amer. Math. Soc. 362 (2010), 3997-4043.
MSC (2010): Primary 57R70; Secondary 58E05, 57R58, 37D15
Posted: March 23, 2010
MathSciNet review: 2608393
Retrieve article in: PDF

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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 -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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