For each positive integer n the HOMFLYPT polynomial of links specializes to a one-variable polynomial that can be recovered from the representation theory of quantum sl(n). For each such n we build a doubly-graded homology theory of links with this polynomial as the Euler characteristic. The core of our construction utilizes the theory of matrix factorizations, which provide a linear algebra description of maximal Cohen-Macaulay modules on isolated hypersurface singularities.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm199-1-1,
author = {Mikhail Khovanov and Lev Rozansky},
title = {Matrix factorizations and link homology},
journal = {Fundamenta Mathematicae},
volume = {201},
year = {2008},
pages = {1-91},
zbl = {1145.57009},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm199-1-1}
}
Mikhail Khovanov; Lev Rozansky. Matrix factorizations and link homology. Fundamenta Mathematicae, Tome 201 (2008) pp. 1-91. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm199-1-1/