Matrix factorizations and link homology

M Khovanov, L Rozansky - arXiv preprint math/0401268, 2004 - arxiv.org
M Khovanov, L Rozansky
arXiv preprint math/0401268, 2004arxiv.org
For each positive integer n the HOMFLY 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.
For each positive integer n the HOMFLY 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.
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