# Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty

## Matrix factorizations and link homology

### Tom 199 / 2008

Fundamenta Mathematicae 199(2008), 1-91 MSC: Primary 57M25. DOI: 10.4064/fm199-1-1

#### Streszczenie

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.

#### Autorzy

• Mikhail KhovanovDepartment of Mathematics
Columbia University
New York, NY 10025, U.S.A.
e-mail
• Lev RozanskyDepartment of Mathematics
University of North Carolina
Chapel Hill, NC 27599, U.S.A.
e-mail

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