Topology Atlas | Conferences

Knots in Washington XXII
May 5-7, 2006
George Washington University
Washington, DC, USA

Organizers
Jozef H. Przytycki (GWU), przytyck@gwu.edu, Yongwu Rong (GWU), rong@gwu.edu, Alexander Shumakovitch (GWU), shurik@gwu.edu

Conference Homepage


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 work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # casv-16.