Matrix factorizations and link homology
- Author(s): Khovanov, Mikhail
- Rozansky, Lev
- et al.
Published Web Locationhttps://arxiv.org/pdf/math/0401268.pdf
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.