Geometry & Topology

Matrix factorizations and link homology II

Mikhail Khovanov and Lev Rozansky

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Abstract

To a presentation of an oriented link as the closure of a braid we assign a complex of bigraded vector spaces. The Euler characteristic of this complex (and of its triply-graded cohomology groups) is the HOMFLYPT polynomial of the link. We show that the dimension of each cohomology group is a link invariant.

Article information

Source
Geom. Topol., Volume 12, Number 3 (2008), 1387-1425.

Dates
Received: 2 February 2006
Revised: 2 April 2008
Accepted: 2 October 2006
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513800100

Digital Object Identifier
doi:10.2140/gt.2008.12.1387

Mathematical Reviews number (MathSciNet)
MR2421131

Zentralblatt MATH identifier
1146.57018

Subjects
Primary: 57M27: Invariants of knots and 3-manifolds
Secondary: 18G99: None of the above, but in this section

Keywords
link homology HOMFLY-PT polynomial

Citation

Khovanov, Mikhail; Rozansky, Lev. Matrix factorizations and link homology II. Geom. Topol. 12 (2008), no. 3, 1387--1425. doi:10.2140/gt.2008.12.1387. https://projecteuclid.org/euclid.gt/1513800100


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