State sum models and homological invariants

Start: 02/02/2011 - 4:15pm
End  : 02/02/2011 - 5:00pm


Adam Lowrance (University of Iowa)


Many classical topological invariants can be expressed as a signed sum over a
set of states. Often one can generalize the classical invariant by replacing the state
sum with a chain complex and taking its homology. In this talk, I will give three
examples of such a construction: 1. Euler characteristic of a CW complex generalized
to cellular homology, 2. the Jones polynomial generalized to Khovanov homology, and
3. the Alexander polynomial generalized to knot Floer homology. I will also discuss
applications of Khovanov homology and knot Floer homology and the relationship
between the two invariants.

Roberts North 15, Claremont McKenna College