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)

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Bar-Natan algebras and modules of oriented surfaces
by
Uwe Kaiser
Boise State University

Asaeda and Frohman initiated the study of Bar-Natan skein modules, which are modules defined from surfaces embedded in 3-manifolds. The (relative) Bar-Natan skein modules of F ×I, for F an oriented surface, can be considered as the modules of a tautological TQFT for the geometric Khovanov homology on surfaces. In this case the Bar-Natan modules are naturally modules over Bar-Natan algebras. I will discuss some recent results and ideas about these modules based on mapping class group action and incompressible surface theory in F ×I. These results should be related with the work of Asaeda, Przytycki and Sikora on Khovanov homology for oriented surfaces.

Date received: March 30, 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-07.