Student Symplectic Seminar: Morse Homology

Seminar | February 27 | 1-2 p.m. | 891 Evans Hall

 Michael Yeh, UC Berkeley

 Department of Mathematics

If $M$ is a compact manifold, a generic smooth function $f:M\to R$ can tell us about the topology of $M$. Classically, one obtains a CW decomposition of $M$ (up to homotopy equivalence) and can then use cellular homology. I will focus on a newer approach which involves constructing a chain complex by counting the flow lines of the gradient of $f$. The resulting homology turns out to be canonically isomorphic to singular homology.