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Affine actions, cohomology and hyperbolicity

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NPC - Non-positive curvature group actions and cohomology

Many groups admit an affine action on a Hilbert, or suitable Banach space which is proper, or at least has an unbounded orbit. For example, CAT cubical groups act properly on Hilbert space; and a hyperbolic group acts properly on an Lp-space, although some cannot act on a Hilbert space with an unbounded orbit (or even without a global fixed point). In the talk I will describe these results and will discuss some recent work, joint with Eric Reckwerdt and Romain Tessera, on the existence of affine actions of relatively hyperbolic groups.



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