Geodesic
The Sigma invariants of Thompson’s group $F$
Robert Bieri1 ; Ross Geoghegan2 ; Dessislava H. Kochloukova3
1Johann Wolfgang Goethe-Universität, Frankfurt am Main, Germany
2Binghamton University, USA
3IMECC - UNICAMP, Campinas, Brazil
Groups, geometry, and dynamics, Tome 4 (2010) no. 2, pp. 263-273

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DOI

Thompson’s group F is the group of all increasing dyadic PL homeomorphisms of the closed unit interval. We compute Σm(F) and Σm(F;Z), the homotopical and homological Bieri–Neumann–Strebel–Renz invariants of F, and show that Σm(F)=Σm(F;Z). As an application, we show that, for every m, F has subgroups of type Fm − 1​ which are not of type FPm​ (thus certainly not of type Fm​).
DOI : 10.4171/ggd/83
Classification : 20-XX, 55-XX, 00-XX
Mots-clés : Thompson’s group, finiteness properties, homological and homotopical Sigma invariants

Robert Bieri  1   ; Ross Geoghegan  2   ; Dessislava H. Kochloukova  3

1 Johann Wolfgang Goethe-Universität, Frankfurt am Main, Germany
2 Binghamton University, USA
3 IMECC - UNICAMP, Campinas, Brazil 
Robert Bieri; Ross Geoghegan; Dessislava H. Kochloukova. The Sigma invariants of Thompson’s group $F$. Groups, geometry, and dynamics, Tome 4 (2010) no. 2, pp. 263-273. doi: 10.4171/ggd/83
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     title = {The {Sigma} invariants of {Thompson{\textquoteright}s} group $F$},
     journal = {Groups, geometry, and dynamics},
     pages = {263--273},
     year = {2010},
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     number = {2},
     doi = {10.4171/ggd/83},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/83/}
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