Faculty of Mathematics
Collaborative Research Centre 701
Spectral Structures and Topological Methods in Mathematics

# Project C8

## Finiteness Properties of Infinite Discrete Groups

Principal Investigator(s) Other Investigators

## Summary:

The main goal is to establish finiteness properties (finite generation, finte presentability, etc.) of arithmetic groups in positive characteristic, e.g., $SL_N(\mathbf{F}_q[t; t^{-1}])$. In particular, one aim is a proof of the {\em Rank Conjecture} which would give the exact finiteness length for reductive groups. Another point on the agenda is the question whether $SL_2(\mathbf{Z}[t; t^{-1}])$ is finitely generated. Finally the finiteness properties of Torelli subgroups (a) in Out($F_{N}$) and (b) in mappingclass groups of closed oriented surfaces are to be determined.

## Recent Preprints:

 13030 Polytopes and groups PDF | PS.GZ 12146 The braided Thompson’s groups are of type $F_\infty$ PDF | PS.GZ 12145 Higher generation for pure braid groups PDF | PS.GZ 12070 The Brin-Thompson groups $sV$ are of type $F_\infty$ PDF | PS.GZ 12069 An Eilenberg–Ganea phenomenon for actions with virtually cyclic stabilisers PDF | PS.GZ 12060 Higher Finiteness Properties of Reductive Arithmetic Groups in Positive Characteristic: The Rank Theorem PDF | PS.GZ 12055 Rational homological stability for groups of partially symmetric automorphisms of free groups PDF | PS.GZ 12054 A combinatorial proof of the degree theorem in Auter space PDF | PS.GZ 12053 Brown's criterion in Bredon homology PDF | PS.GZ 12004 On the classifying space for the family of virtually cyclic subgroups for elementary amenable groups PDF | PS.GZ

## Announced Talks interacting with the project:

 May 21, 2013 16:15U2-135 !!! CANCELLED !!!Endlichkeitseigenschaften arithmetischer Gruppen über Funktionenkörpern (Teil 2)Kai-Uwe Bux May 22, 2013 14:15T2-228 Classifying spaces and cohomology rings for Thompson's groups F and braided FMatthew Zaremsky May 23, 2013 12:15V4-116 Ping-pong on a euclidean buildingStefan Witzel