Matrix factorizations and link homology
Volume 199 / 2008
Fundamenta Mathematicae 199 (2008), 1-91
MSC: Primary 57M25.
DOI: 10.4064/fm199-1-1
Abstract
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.
