Matrix factorizations and link homology

Mikhail Khovanov¹ ; Lev Rozansky²

¹ Department of Mathematics Columbia University New York, NY 10025, U.S.A.
² Department of Mathematics University of North Carolina Chapel Hill, NC 27599, U.S.A.

Fundamenta Mathematicae, Tome 199 (2008) no. 1, pp. 1-91

Résumé

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.

Détail

DOI : 10.4064/fm199-1-1

Keywords: each positive integer homflypt polynomial links specializes one variable polynomial recovered representation theory quantum each build doubly graded homology theory links polynomial euler characteristic core construction utilizes theory matrix factorizations which provide linear algebra description maximal cohen macaulay modules isolated hypersurface singularities