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Twisted multi-distributivity and Lawrence representations of braid groups
by
Victoria Lebed
University of Nantes
Long and Moody suggested an ingenious procedure for transforming a representation of the braid group Bn+1 into a more sophisticated representation of Bn. For instance, their machinery upgrades the trivial representation into the Burau representation, which in turn yields the Lawrence-Krammer representation. Topological and algebraic versions of that procedure were proposed, the latter further developed by Bigelow and Tian. In this talk we will present a simple combinatorial avatar of Bigelow-Tian constructions, using double-layer colorings by what we call Alexander G-quandles. These latter originate from Ishii-Iwakiri-Jang-Oshiro's work on G-families of quandles.
Date received: December 2, 2014
Copyright © 2014 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 # cbjz-26.