Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 7, Number 4 (2007), 1921-1948.
Pseudo-Anosov homeomorphisms and the lower central series of a surface group
Let be the lower central series of a surface group of a compact surface with one boundary component. A simple question to ponder is whether a mapping class of can be determined to be pseudo-Anosov given only the data of its action on for some . In this paper, to each mapping class which acts trivially on , we associate an invariant which is constructed from its action on . We show that if the characteristic polynomial of is irreducible over , then must be pseudo-Anosov. Some explicit mapping classes are then shown to be pseudo-Anosov.
Algebr. Geom. Topol., Volume 7, Number 4 (2007), 1921-1948.
Received: 7 March 2007
Revised: 17 July 2007
Accepted: 24 August 2007
First available in Project Euclid: 20 December 2017
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Malestein, Justin. Pseudo-Anosov homeomorphisms and the lower central series of a surface group. Algebr. Geom. Topol. 7 (2007), no. 4, 1921--1948. doi:10.2140/agt.2007.7.1921. https://projecteuclid.org/euclid.agt/1513796776