Geometry & Topology
- Geom. Topol.
- Volume 13, Number 3 (2009), 1229-1263.
Infinite groups with fixed point properties
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.
Geom. Topol., Volume 13, Number 3 (2009), 1229-1263.
Received: 26 September 2008
Revised: 13 December 2008
Accepted: 12 January 2009
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx] 20F67: Hyperbolic groups and nonpositively curved groups
Secondary: 57S30: Discontinuous groups of transformations 55M20: Fixed points and coincidences [See also 54H25]
Arzhantseva, Goulnara; Bridson, Martin R; Januszkiewicz, Tadeusz; Leary, Ian J; Minasyan, Ashot; None, Jacek. Infinite groups with fixed point properties. Geom. Topol. 13 (2009), no. 3, 1229--1263. doi:10.2140/gt.2009.13.1229. https://projecteuclid.org/euclid.gt/1513800246