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Geometry & Topology 13 (2009) 12291263 1229 Infinite groups with fixed point properties
 

Summary: Geometry & Topology 13 (2009) 1229­1263 1229
Infinite groups with fixed point properties
GOULNARA ARZHANTSEVA
MARTIN R BRIDSON
TADEUSZ JANUSZKIEWICZ
IAN J LEARY
ASHOT MINASYAN
JACEK ´SWIA¸ TKOWSKI
We construct finitely generated groups with strong fixed point properties. Let Xac
be the class of Hausdorff spaces of finite covering dimension which are mod­p
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 2 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 nC2, any proper subset of
which generates a finite p­group.
20F65, 20F67; 57S30, 55M20
Dedicated to Michael W Davis on the occasion of his 60th birthday

  

Source: Arzhantseva, Goulnara N. - Section de Mathématiques, Université de Genève

 

Collections: Mathematics