Year: 2015
Type: article
Abstract: It is known that the Burau representation of the 4-strand braid group is faithful if and only if certain matrices f and k generate a (non-abelian) free group. Regarding f and k as isometries of a Euclidean building, we show that f3 and k3 generate a free group. We give two proofs, one utilizing the metric geometry of the building, and the other using simplicial retractions.
Authors: Stefan Witzel, Matthew C. B. Zaremsky
Institutions: Bielefeld University, Binghamton University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1757112730