Geometry, Topology and Dynamics Seminar
Sheel Ganatra
Stanford University
Open-closed string maps and circle actions in symplectic topology
Abstract: Floer (or pseudoholomorphic curve) theory associates
homological invariants to a symplectic manifold via a (semi-)infinite
form of Morse homology. The resulting structures come in a "closed
string" flavor generalizing quantum cohomology and an "open string"
one known as the Fukaya category.
In this talk, we describe a general program in Floer theory to recover
closed string invariants from open string invariants via "open-closed
string maps", with focus on an extra geometric structure present in
both theories: a chain-level circle action. There is motivation for
understanding such a circle action from both topological field theory
and mirror symmetry, where it is related to the Hodge-to-de Rham
spectral sequence.
Monday October 27, 2014 at 4:00 PM in SEO 612