Topology Atlas | Conferences

Knots in Washington XLV
December 8-10, 2017
George Washington University
Washington, DC, USA

Organizers
Valentina Harizanov (GWU), Jozef H. Przytycki (GWU), Yongwu Rong (GWU), Radmila Sazdanovic (NCSU), Alexander Shumakovitch (GWU), Hao Wu (GWU)

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Colored Khovanov-Rozansky homology of infinite braids
by
Michael Abel
Duke University
Coauthors: Michael Willis (University of California, Los Angeles)

We show that the limiting unicolored sl(N) Khovanov-Rozansky chain complex of any infinite positive braid categorifies a highest-weight projector. This result extends an earlier result of Cautis categorifying highest-weight projectors using the limiting complex of infinite torus braids. Additionally, we show that the results hold in the case of colored HOMFLY-PT Khovanov-Rozansky homology as well. An application of this result is given in finding a partial isomorphism between the HOMFLY-PT homology of any braid positive link and the stable HOMFLY-PT homology of the infinite torus knot as computed by Hogancamp.

Date received: November 18, 2017

Copyright © 2017 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 # cboj-11.