Relative Ends, l^2 Invariants and Property (T)
We establish a splitting theorem for one-ended groups H<g \tilde{e}(g;h)="" such="" that=""> 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 v...
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| Format: | Journal article |
| Language: | English |
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2010
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| _version_ | 1826301063933722624 |
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| author | Kar, A Niblo, G |
| author_facet | Kar, A Niblo, G |
| author_sort | Kar, A |
| collection | OXFORD |
| description | We establish a splitting theorem for one-ended groups H<g \tilde{e}(g;h)="" such="" that=""> 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.</g> |
| first_indexed | 2024-03-07T05:26:42Z |
| format | Journal article |
| id | oxford-uuid:e0cd5877-1b37-47d6-be4d-43d3d31e603b |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T05:26:42Z |
| publishDate | 2010 |
| record_format | dspace |
| spelling | oxford-uuid:e0cd5877-1b37-47d6-be4d-43d3d31e603b2022-03-27T09:50:00ZRelative Ends, l^2 Invariants and Property (T)Journal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:e0cd5877-1b37-47d6-be4d-43d3d31e603bEnglishSymplectic Elements at Oxford2010Kar, ANiblo, GWe establish a splitting theorem for one-ended groups H<g \tilde{e}(g;h)="" such="" that=""> 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.</g> |
| spellingShingle | Kar, A Niblo, G Relative Ends, l^2 Invariants and Property (T) |
| title | Relative Ends, l^2 Invariants and Property (T) |
| title_full | Relative Ends, l^2 Invariants and Property (T) |
| title_fullStr | Relative Ends, l^2 Invariants and Property (T) |
| title_full_unstemmed | Relative Ends, l^2 Invariants and Property (T) |
| title_short | Relative Ends, l^2 Invariants and Property (T) |
| title_sort | relative ends l 2 invariants and property t |
| work_keys_str_mv | AT kara relativeendsl2invariantsandpropertyt AT niblog relativeendsl2invariantsandpropertyt |