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Disoriented and confused: fixing the functoriality of Khovanov homology
by
Scott Morrison
UC Berkeley
Coauthors: Kevin Walker
I’ll describe a modification of Bar-Natan’s 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 document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # casv-16.