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Relative ends, L^2 invariants and Property (T)

By Graham Niblo and Aditi Kar

Abstract

We prove splitting theorems for groups with positive first L^2-betti number (denoted \beta^2_1) and verify Kropholler's conjecture for pairs of groups H \leq G satisfying \beta^2_1(G) &gt; \beta^2_1(H). We also prove that every n-dimensional Poincare duality group containing an (n-1)-dimensional Poincare duality group H with property (T) splits over a subgroup commensurable with H.<br/><br/

Topics: QA
Year: 2011
OAI identifier: oai:eprints.soton.ac.uk:79347
Provided by: e-Prints Soton

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