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The present paper is a summary and overview of results obtained in the author's thesis, "L-2-Betti Numbers of Locally Compact Groups", wherein the definition of L-2-Betti numbers for countable groups is extended to locally compact unimodular groups. In many cases, the L-2-Betti numbers of a lattice are proportional to those of the ambient locally compact group, yielding new results for certain classes of lattices, including arithmetic lattices and Kac-Moody lattices. (C) 2013 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.
Maryna Viazovska, Nihar Prakash Gargava, Vlad Serban