Arzhantseva, Goulnara, Bridson, Martin R., Januszkiewicz, Tadeusz, Leary, Ian J., Minasyan, Ashot and Swiatkowski, Jacek
(2009)
Infinite groups with fixed point properties.
*Geometry & Topology*, 13 (3), 1229-1263.
(doi:10.2140/gt.2009.13.1229).

## Abstract

We construct finitely generated groups with strong fixed point properties. Let Xac be the class of Hausdorff spaces of finite covering dimension which are mod–p acyclic for at least one prime p. We produce the first examples of infinite finitely generated groups Q with the property that for any action of Q on any X ?Xac, there is a global fixed point. Moreover, Q may be chosen to be simple and to have Kazhdan’s property (T). We construct a finitely presented infinite group P that admits no nontrivial action on any manifold in Xac. In building Q, we exhibit new families of hyperbolic groups: for each n ? 1 and each prime p, we construct a nonelementary hyperbolic group Gn,p which has a generating set of size n + 2, any proper subset of which generates a finite p–group.

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- Faculties (pre 2018 reorg) > Faculty of Social, Human and Mathematical Sciences (pre 2018 reorg) > Mathematical Sciences (pre 2018 reorg) > Pure Mathematics (pre 2018 reorg)

Current Faculties > Faculty of Social Sciences > School of Mathematical Sciences > Mathematical Sciences (pre 2018 reorg) > Pure Mathematics (pre 2018 reorg)

School of Mathematical Sciences > Mathematical Sciences (pre 2018 reorg) > Pure Mathematics (pre 2018 reorg) - Current Faculties > Faculty of Social Sciences > School of Mathematical Sciences > Pure Mathematics

School of Mathematical Sciences > Pure Mathematics

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