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.
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页数：16
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