Topology Atlas | Conferences

Knots in Washington XXXVII
January 19-20, 2014
George Washington University
Washington, DC, USA

Mieczyslaw K. Dabkowski (UT Dallas), Valentina Harizanov (GWU), Jozef H. Przytycki (GWU and UMCP), Yongwu Rong (GWU), Radmila Sazdanovic (NCSU), Alexander Shumakovitch (GWU), Hao Wu (GWU)

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A filtration on HOMFLY-PT homology via virtual crossings
Michael Abel
University of North Carolina, Chapel Hill
Coauthors: Lev Rozansky

In 2006, Khovanov gave a construction of HOMFLY-PT homology in the homotopy category of Soergel bimodules. Soergel bimodules can be naturally filtered by bimodules representing virtual crossings, known as standard bimodules. We show that, by choosing the proper filtrations by virtual crossings, we get a filtration on HOMFLY-PT homology which is a link invariant. The grading induced by this filtration is independent of the three preexisting gradings, turning HOMFLY-PT homology into a quadruply-graded theory.

Date received: November 2, 2013

Copyright © 2013 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 # cbid-05.