Morse-Bott homology

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

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 languageEnglish (US)
Pages (from-to)3997-4043
Number of pages47
JournalTransactions of the American Mathematical Society
Volume362
Issue number8
DOIs
StatePublished - Aug 2010

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Morse-Bott homology'. Together they form a unique fingerprint.

Cite this