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2007 Pseudo-Anosov homeomorphisms and the lower central series of a surface group
Justin Malestein
Algebr. Geom. Topol. 7(4): 1921-1948 (2007). DOI: 10.2140/agt.2007.7.1921

Abstract

Let Γk be the lower central series of a surface group Γ 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 ΓΓk for some k. In this paper, to each mapping class f which acts trivially on ΓΓk+1, we associate an invariant Ψk(f) End(H1(S,)) which is constructed from its action on ΓΓk+2 . We show that if the characteristic polynomial of Ψk(f) is irreducible over , then f must be pseudo-Anosov. Some explicit mapping classes are then shown to be pseudo-Anosov.

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Justin Malestein. "Pseudo-Anosov homeomorphisms and the lower central series of a surface group." Algebr. Geom. Topol. 7 (4) 1921 - 1948, 2007. https://doi.org/10.2140/agt.2007.7.1921

Information

Received: 7 March 2007; Revised: 17 July 2007; Accepted: 24 August 2007; Published: 2007
First available in Project Euclid: 20 December 2017

zbMATH: 1197.37056
MathSciNet: MR2366181
Digital Object Identifier: 10.2140/agt.2007.7.1921

Subjects:
Primary: 37E30, 57M60

Rights: Copyright © 2007 Mathematical Sciences Publishers

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Vol.7 • No. 4 • 2007
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