Grid Movie Moves and Combinatorial Knot Floer Homology

Geometry Topology Seminar
Monday, April 16, 2012 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 005
Matt Graham – Brandeis University
John Etnyre
Recently, Sarkar showed that a smooth marked cobordism between two knots K_1 , K_2 induces a map between the knot Floer homology groups of the two knots HFK(K_1 ), HFK(K_2 ). It has been conjectured that this map is well defined (with respect to smooth marked cobordisms). After outlining what needs to be shown to prove this conjecture, I will present my current progress towards showing this result for the combinatorial version of HFK. Specifically, I will present a generalization of Carter and Saito's movie move theorem to grid diagrams, give a very brief introduction to combinatorial knot Floer homology and then present a couple of the required chain homotopies needed for the proof of the conjecture.