2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69913For 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.108 pages, 61 figures, latex, epsQuantum Algebra57M25text