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.
Original language | English (US) |
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Pages (from-to) | 3997-4043 |
Number of pages | 47 |
Journal | Transactions of the American Mathematical Society |
Volume | 362 |
Issue number | 8 |
DOIs | |
State | Published - Aug 2010 |
All Science Journal Classification (ASJC) codes
- General Mathematics
- Applied Mathematics