Matrix factorizations and link homology

Volume 199 / 2008

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


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.


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

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