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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Some differentials on Khovanov–Rozansky homology

Jacob Rasmussen

Geometry & Topology 19 (2015) 3031–3104
Abstract

We study the relationship between the HOMFLY and sl(N) knot homologies introduced by Khovanov and Rozansky. For each N > 0, we show there is a spectral sequence which starts at the HOMFLY homology and converges to the sl(N) homology. As an application, we determine the KR–homology of knots with 9 crossings or fewer.

Keywords
HOMFLY-PT, categorification, Khovanov–Rozansky, differentials
Mathematical Subject Classification 2000
Primary: 57M27
References
Publication
Received: 13 September 2006
Accepted: 21 January 2015
Published: 6 January 2016
Proposed: Peter S Ozsváth
Seconded: Ciprian Manolescu, Haynes Miller
Authors
Jacob Rasmussen
Department of Pure Mathematics and Mathematical Statistics
University of Cambridge
Centre for Mathematical Sciences
Wilberforce Road
Cambridge CB3 0WB
UK