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Matrix factorizations and link homology

Mikhail Khovanov·Lev Rozansky
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Abstract

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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Mikhail Khovanov, Lev Rozansky. 2004-03-22. Matrix factorizations and link homology. https://arxiv.org/abs/math/0401268

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