Authors: Goulnara Arzhantseva, Martin Bridson, Tadeusz Januszkiewicz, 
Ian J Leary, Ashot Minasyan and Jacek \'Swi\c atkowski.  

Goulnara Arzhantseva
Affiliation: Universit\'e de Gen\`eve 

Martin Bridson
Affiliation: Oxford University 

Tadeusz Januszkiewicz 
Affiliation: The Ohio State University and Mathematical Institute of
the Polish Academy of Sciences 

Ian Leary 
Affiliation: The Ohio State University 

Ashot Minasyan 
Affiliation: Universit\'e de Gen\`eve and University of Southampton 

Jacek \'Swi\c atkowski
Affiliation: Uniwersytet Wroclawski

Abstract: We construct finitely generated groups with strong fixed
point properties.  Let ACYC 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 in ACYC, 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 non-trivial
action by diffeomorphisms on any smooth manifold in ACYC.  In
building Q, we exhibit new families of hyperbolic groups: for each
n > 0 and each prime p, we construct a non-elementary hyperbolic
group G_{n,p} which has a generating set of size n+2, any proper
subset of which generates a finite p-group.

Status: preprint