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.
"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