Morse-Bott homology

Details Morse-Bott homology Morse-Bott homology

2006-12-12

arxiv.org/abs/math/0612316v2

Mathematics

Algebraic Topology

53 pages, 4 figures

Scientific paper

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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