Colored Khovanov–Rozansky homology for infinite braids

Abel, Michael; Willis, Michael

doi:10.2140/agt.2019.19.2401

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Colored Khovanov–Rozansky homology for infinite braids

Michael Abel and Michael Willis

Algebraic & Geometric Topology 19 (2019) 2401–2438

DOI: 10.2140/agt.2019.19.2401

Abstract

We show that the limiting unicolored $s l (N)$ 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.

Keywords

Khovanov homology, Khovanov–Rozansky homology, link homology, colored link homology, colored Khovanov–Rozanksy homology, infinite braids, infinite twist

Mathematical Subject Classification 2010

Primary: 57M27

References

Publication

Received: 8 December 2017

Revised: 11 October 2018

Accepted: 26 October 2018

Published: 20 October 2019

Authors

Michael Abel
Department of Mathematics Duke University Durham, NC United States

Michael Willis
Department of Mathematics University of California, Los Angeles Los Angeles, CA United States

Volume 19, issue 5 (2019)