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arXiv:1304.7923 [math.GR]AbstractReferencesReviewsResources

A free subgroup in the image of the 4-strand Burau representation

Stefan Witzel, Matthew C. B. Zaremsky

Published 2013-04-30Version 1

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 f^3 and k^3 generate a free group. We give two proofs, one utilizing the metric geometry of the building, and the other using simplicial retractions.

Comments: 14 pages, 6 figures
Categories: math.GR, math.MG
Subjects: 20F65, 51E24, 57M07
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