Splittings and the asymptotic topology of the lamplighter group
It is known that splittings of finitely presented groups over 2-ended groups can be characterized geometrically. We show that this characterization does not extend to all finitely generated groups. Answering a question of Kleiner we show that the Cayley graph of the lamplighter group is coarsely sep...
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| Format: | Journal article |
| Language: | English |
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2009
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| _version_ | 1797069913921159168 |
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| author | Papasoglu, P |
| author_facet | Papasoglu, P |
| author_sort | Papasoglu, P |
| collection | OXFORD |
| description | It is known that splittings of finitely presented groups over 2-ended groups can be characterized geometrically. We show that this characterization does not extend to all finitely generated groups. Answering a question of Kleiner we show that the Cayley graph of the lamplighter group is coarsely separated by quasi-circles. |
| first_indexed | 2024-03-06T22:31:25Z |
| format | Journal article |
| id | oxford-uuid:586851dd-7d9b-4909-8403-7b0bcdeeab24 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T22:31:25Z |
| publishDate | 2009 |
| record_format | dspace |
| spelling | oxford-uuid:586851dd-7d9b-4909-8403-7b0bcdeeab242022-03-26T17:03:10ZSplittings and the asymptotic topology of the lamplighter groupJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:586851dd-7d9b-4909-8403-7b0bcdeeab24EnglishSymplectic Elements at Oxford2009Papasoglu, PIt is known that splittings of finitely presented groups over 2-ended groups can be characterized geometrically. We show that this characterization does not extend to all finitely generated groups. Answering a question of Kleiner we show that the Cayley graph of the lamplighter group is coarsely separated by quasi-circles. |
| spellingShingle | Papasoglu, P Splittings and the asymptotic topology of the lamplighter group |
| title | Splittings and the asymptotic topology of the lamplighter group |
| title_full | Splittings and the asymptotic topology of the lamplighter group |
| title_fullStr | Splittings and the asymptotic topology of the lamplighter group |
| title_full_unstemmed | Splittings and the asymptotic topology of the lamplighter group |
| title_short | Splittings and the asymptotic topology of the lamplighter group |
| title_sort | splittings and the asymptotic topology of the lamplighter group |
| work_keys_str_mv | AT papasoglup splittingsandtheasymptotictopologyofthelamplightergroup |