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Relative Ends, l^2 Invariants and Property (T)

Abstract:
We establish a splitting theorem for one-ended groups H 2 and the almost malnormal closure of H is a proper subgroup of G. This yields splitting theorems for groups G with non-trivial first l^2 Betti number (\beta^2_1(G)). We verify the Kropholler Conjecture for pairs H < G satisfying \beta^2_1(G) > \beta^2_1(H). We also prove that every n-dimensional Poincare duality (PD^n) group containing a PD^(n-1) group H with property (T) splits over a subgroup commensurable with H.
Publication status:
Published

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Role:
Author
Journal:
JOURNAL OF ALGEBRA
Volume:
333
Issue:
1
Pages:
232-240
Publication date:
2010-03-11
DOI:
EISSN:
1090-266X
ISSN:
0021-8693
URN:
uuid:e0cd5877-1b37-47d6-be4d-43d3d31e603b
Source identifiers:
188462
Local pid:
pubs:188462
Language:
English
Keywords:

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