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Summary and comments to my list of publications Goulnara ARZHANTSEVA, University of Geneva, January 2009
 

Summary: Summary and comments to my list of publications
Goulnara ARZHANTSEVA, University of Geneva, January 2009
Goulnara.Arjantseva@math.unige.ch
[1] 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.
[2] 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

  

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

 

Collections: Mathematics