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arXiv · 1304.7923

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

Stefan Witzel·Matthew C. B. Zaremsky
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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 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.

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Stefan Witzel, Matthew C. B. Zaremsky. 2013-04-30. A free subgroup in the image of the 4-strand Burau representation. https://doi.org/10.1142/s0218216515500650

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