Open Access
2016 Röver's Simple Group Is of Type $F_\infty$
James Belk, Francesco Matucci
Publ. Mat. 60(2): 501-524 (2016). DOI: 10.5565/PUBLMAT_60216_07


We prove that Claas Röver's Thompson-Grigorchuk simple group $V\mathcal{G}$ has type $F_\infty$. The proof involves constructing two complexes on which $V\mathcal{G}$ acts: a simplicial complex analogous to the Stein complex for $V$, and a polysimplicial complex analogous to the Farley complex for $V$. We then analyze the descending links of the polysimplicial complex, using a theorem of Belk and Forrest to prove increasing connectivity.


Download Citation

James Belk. Francesco Matucci. "Röver's Simple Group Is of Type $F_\infty$." Publ. Mat. 60 (2) 501 - 524, 2016.


Received: 19 November 2014; Revised: 29 March 2016; Published: 2016
First available in Project Euclid: 11 July 2016

zbMATH: 1376.20043
MathSciNet: MR3521498
Digital Object Identifier: 10.5565/PUBLMAT_60216_07

Primary: 20E08 , 20F65 , 20J05

Keywords: finiteness properties , Grigorchuk's group , polysimplicial complex , Thompson's groups

Rights: Copyright © 2016 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.60 • No. 2 • 2016
Back to Top