Volume 12, issue 3 (2008)

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Matrix factorizations and link homology II

Mikhail Khovanov and Lev Rozansky

Geometry & Topology 12 (2008) 1387–1425
Abstract

To a presentation of an oriented link as the closure of a braid we assign a complex of bigraded vector spaces. The Euler characteristic of this complex (and of its triply-graded cohomology groups) is the HOMFLYPT polynomial of the link. We show that the dimension of each cohomology group is a link invariant.

Keywords
link homology, HOMFLY-PT polynomial
Mathematical Subject Classification 2000
Primary: 57M27
Secondary: 18G99
References
Publication
Received: 2 February 2006
Revised: 2 April 2008
Accepted: 2 October 2006
Published: 4 June 2008
Proposed: Peter Ozsvath
Seconded: Vaughan Jones, Peter Teichner
Authors
Mikhail Khovanov
Department of Mathematics
Columbia University
New York
NY 10027
Lev Rozansky
Department of Mathematics
University of North Carolina
Chapel Hill
NC 27599