Abstract
We construct finitely generated groups with strong fixed point properties. Let be the class of Hausdorff spaces of finite covering dimension which are mod– acyclic for at least one prime . We produce the first examples of infinite finitely generated groups with the property that for any action of on any , there is a global fixed point. Moreover, may be chosen to be simple and to have Kazhdan’s property (T). We construct a finitely presented infinite group that admits no nontrivial action on any manifold in . In building , we exhibit new families of hyperbolic groups: for each and each prime , we construct a nonelementary hyperbolic group which has a generating set of size , any proper subset of which generates a finite –group.
Citation
Goulnara Arzhantseva. Martin R Bridson. Tadeusz Januszkiewicz. Ian J Leary. Ashot Minasyan. Jacek None. "Infinite groups with fixed point properties." Geom. Topol. 13 (3) 1229 - 1263, 2009. https://doi.org/10.2140/gt.2009.13.1229
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