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

被引：1

作者：

Witzel, Stefan ^{[1
]}

Zaremsky, Matthew C. B. ^{[2
]}

机构：

[1] Univ Bielefeld, Fac Math, D-33501 Bielefeld, Germany

[2] SUNY Binghamton, Dept Math Sci, Binghamton, NY 13902 USA

来源：

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS | 2015年 / 24卷 / 12期

关键词：

Burau representation; braid group; free group; ping-pong; building; BUILDINGS; FAITHFUL;

D O I：

10.1142/S0218216515500650

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页数：16

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