Event Details: Topology/Geometry Seminar - Mathematics and Statistics - Penn State Altoona

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Topology/Geometry Seminar

Twisted Morse Complexes II

Presented by David Hurtubise, Penn State Altoona
Friday, October 25, 2013 | 4:00 PM | 261 Hawthorn

Abstract: The critical points and gradient flow lines of a Morse-Smale function on a compact Riemannian manifold determine a Morse chain complex whose homology is isomorphic to the singular homology of the manifold. Given a closed 1-form on the manifold we can twist the Morse-Smale-Witten boundary operator by integrating the 1-form along the gradient flow lines. In this series of talks I will construct the twisted Morse complex over the real numbers and prove that the homology of the twisted complex depends only on the cohomology class of the closed 1-form. This is joint work with Augustin Banyaga and Peter Spaeth.

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