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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Morse-Bott homology


Authors: Augustin Banyaga and David E. Hurtubise
Journal: Trans. Amer. Math. Soc. 362 (2010), 3997-4043
MSC (2010): Primary 57R70; Secondary 58E05, 57R58, 37D15
Published electronically: March 23, 2010
MathSciNet review: 2608393
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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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Additional Information

Augustin Banyaga
Affiliation: Department of Mathematics, The Pennsylvania State University, University Park, University Park, Pennsylvania 16802
Email: banyaga@math.psu.edu

David E. Hurtubise
Affiliation: Department of Mathematics and Statistics, The Pennsylvania State University, Altoona, Altoona, Pennsylvania 16601-3760
Email: Hurtubise@psu.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-10-05073-7
PII: S 0002-9947(10)05073-7
Received by editor(s): October 11, 2007
Published electronically: March 23, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.