Geometry & Topology 12 (2008) 1387–1425

DOI: 10.2140/gt.2008.12.1387

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

Primary: 57M27

Secondary: 18G99

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

References

Authors