- 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
- Publisher copy:
- 10.1016/j.jalgebra.2011.02.030
-
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- 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
- Copyright date:
- 2010
Journal article
Relative Ends, l^2 Invariants and Property (T)
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