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The evolution of L2-Betti numbers

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NPCW05 - Group actions and cohomology in non-positive curvature

L2-Betti numbers of Riemannian manifolds were introduced by Atiyah in the 1970s. Cheeger and Gromov extended their scope of definition to all countable discrete groups in the 1980s. Nowadays, there are L2-Betti numbers of arbitrary spaces with arbitrary discrete group actions, of locally compact groups, of quantum groups, of von Neumann algebras, of measured equivalence relations and of invariant random subgroups. Their relation to classical homology comes via a remarkable theorem of Lück, the approximation theorem. We sketch the remarkable extension of the  definition of L2-Betti numbers and present some results about totally disconnected groups. The latter is based on joint work with Henrik Petersen and Andreas Thom. 

This talk is part of the Isaac Newton Institute Seminar Series series.

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