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.
"Matrix factorizations and link homology II." Geom. Topol. 12 (3) 1387 - 1425, 2008. https://doi.org/10.2140/gt.2008.12.1387