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Khovanov homology and restricted isotopies
by
Benjamin Audoux
Université Paul Sabatier, Toulouse, France
Coauthors: Thomas Fiedler
Usually, knots are given by diagrams and isotopies by sequences of Reidemeister moves. According to the orientation, one can distinguish two Reidemeister moves of type II and eight of type III. By forbiding some of them, we define some restricted notion of isotopies of links, that is braid-like and star-like isotopies.
Jones polynomial and Khovanov homology can be refined in order to be invariant only under these isotopies. Studying them may shed new light on internal mechanism of usual Khovanov homology.
Paper reference: arXiv:math.GT/0503080
Date received: November 20, 2005
Copyright © 2005 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # carw-06.