The Sigma Invariants of Thompson's Group F

By R. Bieri, R. Geoghegan, D. Kochloukova. 2008

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Thompson's group F is the group of all increasing dyadic piecewise linear homeomorphisms of the closed unit interval. We compute Sigma^m(F) and Sigma^m(F;Z), the homotopical and homological Bieri-Neumann-Strebel-Renz invariants of F, and we show that Sigma^m(F) = Sigma^m(F;Z). As an application, we show that, for every m, F has subgroups of type F_{m-1} which are not of type F_{m}.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a6a09b2d443fda65c674c6f4335747365782b163