2007/01/31 by David Clark, Scott Morrison, Kevin Walker
Mathematics · #Advanced Combinatorial Mathematics #Algebra over a field #Geometric and Algebraic Topology #Hochschild homology #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Khovanov homology #Link (geometry) #math.GT #msc:57M25 #msc:57M27 #msc:57Q45
paper · pdf · doi:10.2140/gt.2009.13.1499
published as Geom. Topol. 13 (2009) 1499-1582 · 91 pages. Added David Clark as co-author. Further detail on variations of third Reidemeister moves, to allow treatment of previously missing cases of movie move six. See changelog section for more detail
arxiv created 2008/01/21 · openalex publication_date 2009/03/03 · arxiv updated 2014/11/11 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We describe a modification of Khovanov homology This requires introducing "disorientations" in the category of smoothings and abstract cobordisms between them used in Bar-Natan's definition. Disorientations have "seams" separating oppositely oriented regions, coming with a preferred normal direction. The seams satisfy certain relations (just as the underlying cobordisms satisfy relations such as the neck cutting relation).