# Geometric Analysis and Topology Seminar

#### Combinatorial Heegaard-Floer Invariants for Four-Dimensional Cobordisms

Speaker: Ciprian Manolescu, Columbia

Location: Warren Weaver Hall 813

Date: Friday, April 13, 2007, 11 a.m.

Synopsis:

Hat Heegaard Floer theory assigns a finitely generated abelian group to each three-manifold, and a group homomorphism to each (decorated) four-dimensional cobordism. The corresponding hat invariants for closed 4-manifolds are trivial, but for 4-manifolds with boundary they are strong enough to detect exotic smooth structures. Last summer Sarkar and Wang gave a combinatorial description of the hat invariants for 3-manifolds. I will talk about joint work with Lipshitz and Wang, in which we described combinatorially the hat invariants for cobordisms.