## 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.