#### Volume 19, issue 6 (2015)

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Some differentials on Khovanov–Rozansky homology

### Jacob Rasmussen

Geometry & Topology 19 (2015) 3031–3104
##### Abstract

We study the relationship between the HOMFLY and $\mathit{sl}\left(N\right)$ 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 $\mathit{sl}\left(N\right)$ homology. As an application, we determine the KR–homology of knots with 9 crossings or fewer.

##### Keywords
HOMFLY-PT, categorification, Khovanov–Rozansky, differentials
Primary: 57M27
##### 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