Summary: Summary and comments to my list of publications
Goulnara ARZHANTSEVA, University of Geneva, January 2009
 G. N. Arzhantseva, M. Bridson, T. Januszkiewicz, I. Leary, A. Minasyan, J. Swiatkowski,
Infinite groups with fixed point properties, Geometry & Topology, (2009), to appear.
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 non-trivial action by diffeomorphisms on any
smooth manifold in Xac. In building Q, we exhibit new families of hyperbolic groups: for
each n 1 and each prime p, we construct a non-elementary hyperbolic group Gn,p which
has a generating set of size n + 2, any proper subset of which generates a finite p-group.
 G. N. Arzhantseva, C. Drut¸u, and M. Sapir, Compression functions of uniform embed-
dings of groups into Hilbert and Banach spaces, Journal f¨ur die Reine und Angewandte
Mathematik, [Crelle's Journal], (2008), in press.
We construct finitely generated groups with arbitrary prescribed Hilbert space compres-
sion [0, 1]. This answers a question of E. Guentner and G. Niblo. For a large class
of Banach spaces E (including all uniformly convex Banach spaces), the Ecompression of