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arXiv · 0807.5138

The Sigma Invariants of Thompson's Group F

Robert Bieri·Ross Geoghegan·Dessislava Kochloukova
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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}.

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Robert Bieri, Ross Geoghegan, Dessislava Kochloukova. 2008-07-31. The Sigma Invariants of Thompson's Group F. https://arxiv.org/abs/0807.5138

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