Orientations of Chord Diagrams and Khovanov Homology

Details Orientations of Chord Diagrams and Khovanov Homology Orientations of Chord Diagrams and Khovanov Homology

2006-11-13

arxiv.org/abs/math/0611406v2

2005 Gokova Geometry/Topology Conference Proceedings, 2006, pp. 184 - 209

Mathematics

Geometric Topology

Added references and post-publication remarks

Scientific paper

By adding or removing appropriate structures to Gauss diagram, one can create useful objects related to virtual links. In this paper few objects of this kind are studied: twisted virtual links generalizing virtual links; signed chord diagrams staying halfway between twisted virtual links and Kauffman bracket / Khovanov homology; alternatable virtual links intermediate between virtual and classical links. The most profound role here belongs to a structure that we dare to call orientation of chord diagram. Khovanov homology is generalized to oriented signed chord diagrams and links in oriented thickened surface such that the link projection realizes the first Stiefel-Whitney class of the surface. After this paper was published, V.O.Manturov succeeded in extending Khovanov homology with arbitrary coefficients to arbitrary virtual links, see arXiv: math.GT/0601152.

Affiliated with

Also associated with

No associations

Rating

Orientations of Chord Diagrams and Khovanov Homology does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Orientations of Chord Diagrams and Khovanov Homology, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Orientations of Chord Diagrams and Khovanov Homology will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-488021