Controlled embeddings into groups that have no non-trivial finite quotients
If a class of finitely generated groups Curly(G) is closed under isometric amalgamations along free subgroups, then every G in Curly(G) can be quasi-isometrically embedded in a group Hat(G) in Curly(G) that has no proper subgroups of finite index. Every compact, connected, non-positively curved sp...
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| Format: | Journal article |
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1998
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| _version_ | 1797078556989194240 |
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| author | Bridson, M |
| author_facet | Bridson, M |
| author_sort | Bridson, M |
| collection | OXFORD |
| description | If a class of finitely generated groups Curly(G) is closed under isometric amalgamations along free subgroups, then every G in Curly(G) can be quasi-isometrically embedded in a group Hat(G) in Curly(G) that has no proper subgroups of finite index. Every compact, connected, non-positively curved space X admits an isometric embedding into a compact, connected, non-positively curved space Overline(X) such that Overline(X) has no non-trivial finite-sheeted coverings. |
| first_indexed | 2024-03-07T00:33:35Z |
| format | Journal article |
| id | oxford-uuid:80a7c1a7-5a9e-4aa9-a1f1-138c462e3cd9 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T00:33:35Z |
| publishDate | 1998 |
| record_format | dspace |
| spelling | oxford-uuid:80a7c1a7-5a9e-4aa9-a1f1-138c462e3cd92022-03-26T21:24:45ZControlled embeddings into groups that have no non-trivial finite quotientsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:80a7c1a7-5a9e-4aa9-a1f1-138c462e3cd9Symplectic Elements at Oxford1998Bridson, MIf a class of finitely generated groups Curly(G) is closed under isometric amalgamations along free subgroups, then every G in Curly(G) can be quasi-isometrically embedded in a group Hat(G) in Curly(G) that has no proper subgroups of finite index. Every compact, connected, non-positively curved space X admits an isometric embedding into a compact, connected, non-positively curved space Overline(X) such that Overline(X) has no non-trivial finite-sheeted coverings. |
| spellingShingle | Bridson, M Controlled embeddings into groups that have no non-trivial finite quotients |
| title | Controlled embeddings into groups that have no non-trivial finite
quotients |
| title_full | Controlled embeddings into groups that have no non-trivial finite
quotients |
| title_fullStr | Controlled embeddings into groups that have no non-trivial finite
quotients |
| title_full_unstemmed | Controlled embeddings into groups that have no non-trivial finite
quotients |
| title_short | Controlled embeddings into groups that have no non-trivial finite
quotients |
| title_sort | controlled embeddings into groups that have no non trivial finite quotients |
| work_keys_str_mv | AT bridsonm controlledembeddingsintogroupsthathavenonontrivialfinitequotients |