Matrix factorizations and link homology II

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.

37 pages, 20 figures; version 2 corrects an inaccuracy in the proof of Proposition 3

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• Categorification of the Kauffman bracket skein module of I-bundles over surfaces
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