|
Organizers |
Disoriented and confused: fixing the functoriality of Khovanov homology
by
Scott Morrison
UC Berkeley
Coauthors: Kevin Walker
Ill describe a modification of Bar-Natans cobordism model for Khovanov homology, introducing disorientations, and some rules for manipulating them. Using these, we discover that link cobordisms now induce honest well-defined maps between the complexes associated to links, not just up-to-sign maps.
In addition to disorientations, we can also add confusions: places where a disorientation changes type. These live up to their name; they need a spin framing, and change sign when rotated. However, they fix a few defects of the disoriented model, allow nice proofs, and make contact with some familiar features of su(2)s planar representation theory.
There will be lots of pictures!
Date received: May 3, 2006
Copyright © 2006 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 # casv-16.