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On the Colored Jones Polynomial and Floer homology
by
Elisenda Grigsby
Columbia University
Coauthors: Stephan Wehrli
The relationship between categorifications of quantum knot polynomials and Floer homology invariants is intriguing and still poorly-understood. In this talk, we will discuss a connection between Khovanov's categorification of the reduced n-colored Jones polynomial and sutured Floer homology, a relative version of Heegaard Floer homology recently developed by Andras Juhasz. As an application, we prove that Khovanov's categorification detects the unknot when n > 1.
Date received: May 3, 2008
Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caxb-11.