- Working Paper
We define a bounded cohomology class, called the median class, in the second bounded cohomology -- with appropriate coefficients -- of the automorphism group of a finite imensional CAT(0) cube complex X. This in turn defines the median class of an action of \Gamma\ by tomorphisms of X.<br> We show that the median class of a non-elementary action by automorphisms does not vanish. We apply this result to establish a superrigidity result and show for example that no irreducible attice in SL(2,R)xSL(2,R), or more generally in the product of at least two locally compact groups with finitely many connected components, can act non-elementarily on a finite dimensional CAT(0) cube complex. In the course of the proof we construct a \Gamma-equivariant measurable map from a Poisson boundary of \Gamma\ with values in the non-terminating ultrafilters on the Roller boundary of X Show more
Organisational unit08802 - Iozzi, Alessandra (Tit.-Prof.)
NotesSubmitted on 7 Dec 2012 (v1). See also: http://e-citations.ethbib.ethz.ch/view/pub:123249.
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