Geometry & Topology

Some differentials on Khovanov–Rozansky homology

Jacob Rasmussen

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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.

Article information

Source
Geom. Topol., Volume 19, Number 6 (2015), 3031-3104.

Dates
Received: 13 September 2006
Accepted: 21 January 2015
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1510858870

Digital Object Identifier
doi:10.2140/gt.2015.19.3031

Mathematical Reviews number (MathSciNet)
MR3447099

Zentralblatt MATH identifier
06533809

Subjects
Primary: 57M27: Invariants of knots and 3-manifolds

Keywords
HOMFLY-PT categorification Khovanov–Rozansky differentials

Citation

Rasmussen, Jacob. Some differentials on Khovanov–Rozansky homology. Geom. Topol. 19 (2015), no. 6, 3031--3104. doi:10.2140/gt.2015.19.3031. https://projecteuclid.org/euclid.gt/1510858870


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