Matrix factorizations and link homology

Details Matrix factorizations and link homology Matrix factorizations and link homology

2004-01-21

arxiv.org/abs/math/0401268v2

Mathematics

Quantum Algebra

108 pages, 61 figures, latex, eps

Scientific paper

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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