The Sigma Invariants of Thompson's Group F

@article{Bieri2008TheSI,
  title={The Sigma Invariants of Thompson's Group F},
  author={R. Bieri and R. Geoghegan and D. Kochloukova},
  journal={arXiv: Group Theory},
  year={2008}
}
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}. 

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