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A second time around the Volume Conjecture
May 30 - June 3, 2007
Louisiana State University
Baton Rouge, LA, USA

Organizers
Abhijit Champanerkar, Oliver Dasbach, Effie Kalfagianni, Ilya Kofman, Walter Neumann, Neal Stoltzfus

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Khovanov homology for concatenation of tangles
by
Adam S Sikora
SUNY Buffalo

Khovanov defined homology theory for links and later generalized it to tangles. Other versions of tangle homology were proposed by Bar-Natan and Asaeda-Przytycki-Sikora. Unfortunately, in all of these theories, homology groups of tangles T_1 and T_2 do not determine the homologies of the link obtained by full concatenation of T_1 and T_2.

We propose a stronger version of homology theory for tangles which solves this problem - we prove a Kunneth-type formula for our homology, expressing homology of (T_1 cup T_2) by homologies of T_1 and of T_2.

Date received: May 15, 2007

Copyright © 2007 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 # caus-10.