Surgery Formulas and Heegaard Floer Homology of Mapping Tori

Geometry Topology Seminar
Monday, September 27, 2010 - 17:00
1 hour (actually 50 minutes)
Skiles 269
University of Georgia

This is the second talk in the Emory-Ga Tech-UGA joint seminar. The first talk will begin at 3:45. 

 There are many conjectured connections between Heegaard Floer homology and the various homologies appearing in low dimensional topology and symplectic geometry.  One of these conjectures states, roughly, that if \phi is a diffeomorphism of a closed Riemann surface, a certain portion of the Heegaard Floer homology of the mapping torus of \phi should be equal to the Symplectic Floer homology of \phi.  I will discuss how this can be confirmed when \phi is periodic (i.e., when some iterate of \phi is the identity map).  I will recall how a mapping torus can be realized via Dehn surgery; then, I will sketch how the surgery long exact triangles of Heegaard Floer homology can be distilled into more direct surgery formulas involving knot Floer homology.  Finally, I'll say a few words about what actually happens when you use these formulas for the aforementioned Dehn surgeries: a "really big game of tic-tac-toe".