Topology Atlas | Conferences

Knots in Washington XXXIII; Categorification of Knots, Algebras, and Quandles; Quantum Computing
December 2-4, 2011
George Washington University
Washington, DC, USA

Organizers
Valentina Harizanov (GWU),Mark Kidwell (U.S. Naval Academy and GWU), Jozef H. Przytycki (GWU), Yongwu Rong (GWU), Radmila Sazdanovic (U.Penn), Alexander Shumakovitch (GWU), Hao Wu (GWU)

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Grid Movie Moves and Combinatorial Knot Floer Homology
by
Matthew Graham
Brandeis University

Recently, Sarkar showed that a smooth marked cobordism between two knots K1, K2 induces a map between the knot Floer homology groups of the two knots HFK(K1), HFK(K2). 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.

Date received: November 14, 2011

Copyright © 2011 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbdt-19.