Topology Atlas | Conferences

Knots in Washington XXXV
December 7-9, 2012
George Washington University
Washington, DC, USA

Organizers
Mieczyslaw K. Dabkowski (UT Dallas), Valentina Harizanov (GWU), Jozef H. Przytycki (GWU), Yongwu Rong (GWU), Radmila Sazdanovic (U.Penn), Alexander Shumakovitch (GWU), Hao Wu (GWU)

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Hochschild, Chevalley-Eilenberg and quandle homologies are braided homologies
by
Victoria Lebed
Université Paris 7, IMJ

In this talk we present a homology theory for braided objects in monoidal categories. We give a construction in terms of quantum co-shuffles and then refine the differential structure to get a presimplicial one, weakly simplicial if the braided object is endowed with a compatible comultiplication. Explicit formulas will be given using the graphical calculus. Several remarkable features of the braided homologies will be discussed.

On the other hand, we interpret associative, Leibniz/Lie and quandle structures in terms of braidings. Braided homology theories for these ``structural'' braidings include familiar homologies for the corresponding structures.

Date received: October 9, 2012

Copyright © 2012 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 # cbfw-03.