English

The Sigma Invariants of Thompson's Group F

Group Theory 2008-08-01 v1 Algebraic Topology

Abstract

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}.

Keywords

Cite

@article{arxiv.0807.5138,
  title  = {The Sigma Invariants of Thompson's Group F},
  author = {Robert Bieri and Ross Geoghegan and Dessislava Kochloukova},
  journal= {arXiv preprint arXiv:0807.5138},
  year   = {2008}
}

Comments

9 pages