Group splittings and asymptotic topology
It is a consequence of the theorem of Stallings on groups with many ends that splittings over finite groups are preserved by quasi-isometries. In this paper we use asymptotic topology to show that group splittings are preserved by quasi-isometries in many cases. Roughly speaking we show that splitti...
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| Format: | Journal article |
| Language: | English |
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2002
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| _version_ | 1826281627154644992 |
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| author | Papasoglu, P |
| author_facet | Papasoglu, P |
| author_sort | Papasoglu, P |
| collection | OXFORD |
| description | It is a consequence of the theorem of Stallings on groups with many ends that splittings over finite groups are preserved by quasi-isometries. In this paper we use asymptotic topology to show that group splittings are preserved by quasi-isometries in many cases. Roughly speaking we show that splittings are preserved under quasi-isometries when the vertex groups are fundamental groups of aspherical manifolds (or more generally `coarse PD(n)-groups') and the edge groups are `smaller' than the vertex groups. |
| first_indexed | 2024-03-07T00:31:38Z |
| format | Journal article |
| id | oxford-uuid:7fff9f47-d1f5-486c-ac4b-8cf489279082 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T00:31:38Z |
| publishDate | 2002 |
| record_format | dspace |
| spelling | oxford-uuid:7fff9f47-d1f5-486c-ac4b-8cf4892790822022-03-26T21:20:28ZGroup splittings and asymptotic topologyJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:7fff9f47-d1f5-486c-ac4b-8cf489279082EnglishSymplectic Elements at Oxford2002Papasoglu, PIt is a consequence of the theorem of Stallings on groups with many ends that splittings over finite groups are preserved by quasi-isometries. In this paper we use asymptotic topology to show that group splittings are preserved by quasi-isometries in many cases. Roughly speaking we show that splittings are preserved under quasi-isometries when the vertex groups are fundamental groups of aspherical manifolds (or more generally `coarse PD(n)-groups') and the edge groups are `smaller' than the vertex groups. |
| spellingShingle | Papasoglu, P Group splittings and asymptotic topology |
| title | Group splittings and asymptotic topology |
| title_full | Group splittings and asymptotic topology |
| title_fullStr | Group splittings and asymptotic topology |
| title_full_unstemmed | Group splittings and asymptotic topology |
| title_short | Group splittings and asymptotic topology |
| title_sort | group splittings and asymptotic topology |
| work_keys_str_mv | AT papasoglup groupsplittingsandasymptotictopology |