2005/05/31 by Mikhail Khovanov, Lev Rozansky · 5 citations
Mathematics · #Advanced Combinatorial Mathematics #Braid #Closure (psychology) #Cohomology #Dimension (graph theory) #Equivariant cohomology #Euler characteristic #Geometric and Algebraic Topology #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Link (geometry) #Polynomial #math.GT #math.QA #msc:57M25
paper · pdf · doi:10.2140/gt.2008.12.1387
published as Geom. Topol. 12 (2008) 1387-1425 · 37 pages, 20 figures; version 2 corrects an inaccuracy in the proof of Proposition 3
arxiv created 2006/01/31 · openalex publication_date 2008/06/04 · arxiv updated 2014/11/11 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 triplygraded cohomology groups) is the HOMFLYPT polynomial of the link. We show that the dimension of each cohomology group is a link invariant.