Some differentials on Khovanov–Rozansky homology

Rasmussen, Jacob

doi:10.2140/gt.2015.19.3031

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Some differentials on Khovanov–Rozansky homology

Jacob Rasmussen

Geometry & Topology 19 (2015) 3031–3104

DOI: 10.2140/gt.2015.19.3031

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

Volume 19, issue 6 (2015)