|
Organizers |
Looking for non-zero maps between isomorphism classes of tangles
by
Robert Todd
University of Nebraska Omaha
A cobordism between two links L1 and L2 induces a map between the Kh(L1) and Kh(L2). Dror Bar-Natan gave a way to talk about cobordisms between tangles and the maps that they induce on the complexes associated to these tangles. Given two knots it is clear what are all possible non-zero maps from the Khovanov homology of one to the Khovanov homology other. Here we given a homology theory on surfaces which allows one to determine all possible chain maps between Bar-Natan's tangle complexes that induce non-zero maps on the isomorphism classes of the tangles. As an example we derive the maps associated to the Reidemeister moves.
Date received: March 27, 2008
Copyright © 2008 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 # cawt-16.