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Abstract

Together with G. Arzhantseva, M Bridson, I Leary, A.Minasyan and 
J.Swiatkowski we construct sevaral groups having fixed point property for 
actions. Probably the most dramatic is an example of an infinite group
which, has a fixed point for any action on a finite dimensional 
contractible space.
The construction involves certain systolic simplices of groups.
As this seems to have some independent interest, I want to explain it in 
some detail. Hopefully Ian will explain other aspects of the paper.