Topology Atlas | Conferences

KNOTS in WASHINGTON XV (2nd Japan-USA Workshop in Knot Theory)
January 10-15, 2003
George Washington University and Johns Hopkins University
Washington, DC and Baltimore, MD, USA

Organizers
Kazuaki Kobayashi, Jozef H. Przytycki, Yongwu Rong, Shin-ichi Suzuki, Kouki Taniyama, Tatsuya Tsukamoto, Akira Yasuhara

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Construction of Braid Representations Through Hyperplane Arrangements
by
Ofer Ron
Hebrew University of Jerusalem, Giv'at Ram
Coauthors: Advised by Prof. Ruth Lawrence

We construct a fiber bundle F → E → Xn (where Xn is the configuration space of n ordered points) using the configuration space of a set of hyperplanes as the fiber, and provide a section. Using this we obtain a homomorphism Pn=\pi1(Xn) → \Aut(\pi1(F)) which we then translate into a homomorphism on the first homology (with a twisted local coefficient system) of the fiber, thus obtaining a representation of Pn.

We will present the complete construction of representations for Pn using the configuration space of n hyperplanes in complex (n-2) dimensional space, which may be conjugate to the Burau representation, and point out the difficulties in the computation of the possibly more interesting representation using the configuration space of n lines in complex 2 dimensional space.

Date received: January 10, 2003

Copyright © 2003 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 # cajr-38.