Topology Atlas | Conferences

Knots in Washington XXIV; Dedicated to the memory of Xiao-Song Lin
April 13-15, 2007
George Washington University
Washington, DC, USA

Organizers
Jozef H. Przytycki (GWU and UMD), Yongwu Rong (GWU), Alexander Shumakovitch (GWU)

Conference Homepage


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 homology theories, homology of tangles T_1 and T_2 seem not to determine the homologies of the link T_1 cup T_2 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: April 6, 2007

Copyright © 2007 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 # cauq-11.