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