Topology Atlas | Conferences

Knots in Washington XXVII; 3rd Japan-USA Workshop in Knot Theory
January 9-11, 2009
George Washington University
Washington, DC, USA

Organizers
Yoshiyuki Ohyama (TWCU), Jozef H. Przytycki (GWU), Yongwu Rong (GWU), Alexander Shumakovitch (GWU), Kouki Taniyama (Waseda and GWU), Tatsuya Tsukamoto (Osaka IT), Hao Wu (GWU), Akira Yasuhara (Tokyo GU)

Conference Homepage


Bar-Natan modules and Bar-Natan pairings of oriented 3-manifolds
by
Uwe Kaiser
Boise State University

We discuss sesquilinear pairings defined by Bar-Natan modules (and their generalizations using general Frobenius algebras), which descend from universal manifold pairings recently discussed by Calegari, Freedman, Walker and others. Such a Bar-Natan pairing exists for each oriented closed surface with an embedded oriented closed 1-manifold (and each Frobenius algebra with involution). We also discuss how the Heegaard genus of closed 3-manifolds naturally appears in the calculation of Bar-Natan modules, and more generally how the calculation of Bar-Natan modules is related with the geometric topology of the 3-manifold.

Date received: November 28, 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 # caxq-38.