Relative ends, L^2 invariants and Property (T)
Relative ends, L^2 invariants and Property (T)
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) > \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.
L2 betti numbers, stallings' theorem, splittings of groups, end invariants, ends of pairs of groups, codimension 1 subgroups, kazhdan's property (T)
232-240
Niblo, Graham
43fe9561-c483-4cdf-bee5-0de388b78944
Kar, Aditi
af416da5-c2ae-4f05-b692-758dc4a9bf69
1 May 2011
Niblo, Graham
43fe9561-c483-4cdf-bee5-0de388b78944
Kar, Aditi
af416da5-c2ae-4f05-b692-758dc4a9bf69
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) > \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.
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Submitted date: 12 March 2010
Published date: 1 May 2011
Keywords:
L2 betti numbers, stallings' theorem, splittings of groups, end invariants, ends of pairs of groups, codimension 1 subgroups, kazhdan's property (T)
Organisations:
Pure Mathematics
Identifiers
Local EPrints ID: 79347
URI: http://eprints.soton.ac.uk/id/eprint/79347
ISSN: 0021-8693
PURE UUID: 9c333d08-9c42-4bf0-a02c-fcf834b45c62
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Date deposited: 12 Mar 2010
Last modified: 14 Mar 2024 02:36
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Author:
Aditi Kar
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