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Topology/Geometry Seminar
Thursday, December 7, 2006
5:05pm,
106 McAllister
David Hurtubise
Penn State Altoona
A New Proof of the Morse-Bott Homology Theorem.
Abstract: We construct a chain complex associated to a Morse-Bott function on a finite dimensional compact oriented smooth Riemannian manifold meeting certain transversality assumptions. This Morse-Bott-Smale chain complex reduces to the Morse-Smale-Witten chain complex when the function is Morse-Smale and to the chain complex of smooth singular cubes when the function is constant. Using compactified moduli spaces of time dependent gradient flow lines we prove a continuation theorem asserting that the homology of the Morse-Bott-Smale chain complex is independent of the Morse-Bott function used to define the complex.This proves that the homology of both the Morse-Bott-Smale chain complex and the Morse-Smale-Witten chain complex are isomorphic to the singular homology of the manifold with integer coefficients and gives a new proof of the Morse Homology Theorem.
We meet weekly on Thursday afternoons, with the third meeting of each month in Altoona. If you are interested in giving a talk in our seminar please contact one of the coordinators for the Spring 2006 semester: Aissa Wade and Wojciech Dorabiala.
