Pseudo-Anosov homeomorphisms and the lower central series of a surface group

被引:2
|
作者
Malestein, Justin [1 ]
机构
[1] Univ Chicago, Dept Math, Chicago, IL 60637 USA
来源
ALGEBRAIC AND GEOMETRIC TOPOLOGY | 2007年 / 7卷
关键词
D O I
10.2140/agt.2007.7.1921
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let Gamma(k) be the lower central series of a surface group Gamma of a compact surface S with one boundary component. A simple question to ponder is whether a mapping class of S can be determined to be pseudo-Anosov given only the data of its action on Gamma/Gamma(k) for some k. In this paper, to each mapping class f which acts trivially on Gamma/Gamma(k+l), we associate an invariant Psi(k)(f) epsilon End(H-1(S, Z)) which is constructed from its action on Gamma/Gamma(k+2). We show that if the characteristic polynomial Of Psi(k)(f) is irreducible over Z, then f must be pseudo-Anosov. Some explicit mapping classes are then shown to be pseudo-Anosov.
引用
收藏
页码:1921 / 1948
页数:28
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