- 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 dimensional CAT(0) cube complex X. The median class of X behaves naturally with respect to taking products and appropriate subcomplexes and defines in turn the "median class of an action" by automorphisms of X.<br> We show that the median class of a non-elementary action by automorphisms does not vanish and we show to which extent it does vanish if the action is elementary. We apply this result to establish a superrigidity result and show for example that no irreducible lattice in SL(2,R)x SL(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 Γ -equivariant measurable map from a Poisson boundary of Γ with values in the non-terminating ultrafilters on the Roller boundary of X. Show more
Pages / Article No.
Organisational unit08802 - Iozzi, Alessandra (Tit.-Prof.)
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Is previous version of: http://hdl.handle.net/20.500.11850/117300
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