Quasi‐isometry invariance of group splittings over coarse Poincaré duality groups
We show that if G is a group of type F P n + 1 Z 2 that is coarsely separated into three essential, coarse disjoint, coarse complementary components by a coarse P D n Z 2 space W , then W is at finite Hausdorff distance from a subgroup H of G ; moreover, G splits over a subgroup commensurable to a s...
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| Format: | Journal article |
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Wiley
2018
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| _version_ | 1826258748395487232 |
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| author | Margolis, A |
| author_facet | Margolis, A |
| author_sort | Margolis, A |
| collection | OXFORD |
| description | We show that if G is a group of type F P n + 1 Z 2 that is coarsely separated into three essential, coarse disjoint, coarse complementary components by a coarse P D n Z 2 space W , then W is at finite Hausdorff distance from a subgroup H of G ; moreover, G splits over a subgroup commensurable to a subgroup of H . We use this to deduce that splittings of the form G = A ∗ H B , where G is of type F P n + 1 Z 2 and H is a coarse P D n Z 2 group such that both | Comm A ( H ) : H | and | Comm B ( H ) : H | are greater than two, are invariant under quasi‐isometry. |
| first_indexed | 2024-03-06T18:38:53Z |
| format | Journal article |
| id | oxford-uuid:0c3761e4-6c0c-4765-b75b-dd9c5aee5628 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T18:38:53Z |
| publishDate | 2018 |
| publisher | Wiley |
| record_format | dspace |
| spelling | oxford-uuid:0c3761e4-6c0c-4765-b75b-dd9c5aee56282022-03-26T09:33:44ZQuasi‐isometry invariance of group splittings over coarse Poincaré duality groupsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:0c3761e4-6c0c-4765-b75b-dd9c5aee5628Symplectic Elements at OxfordWiley2018Margolis, AWe show that if G is a group of type F P n + 1 Z 2 that is coarsely separated into three essential, coarse disjoint, coarse complementary components by a coarse P D n Z 2 space W , then W is at finite Hausdorff distance from a subgroup H of G ; moreover, G splits over a subgroup commensurable to a subgroup of H . We use this to deduce that splittings of the form G = A ∗ H B , where G is of type F P n + 1 Z 2 and H is a coarse P D n Z 2 group such that both | Comm A ( H ) : H | and | Comm B ( H ) : H | are greater than two, are invariant under quasi‐isometry. |
| spellingShingle | Margolis, A Quasi‐isometry invariance of group splittings over coarse Poincaré duality groups |
| title | Quasi‐isometry invariance of group splittings over coarse Poincaré duality groups |
| title_full | Quasi‐isometry invariance of group splittings over coarse Poincaré duality groups |
| title_fullStr | Quasi‐isometry invariance of group splittings over coarse Poincaré duality groups |
| title_full_unstemmed | Quasi‐isometry invariance of group splittings over coarse Poincaré duality groups |
| title_short | Quasi‐isometry invariance of group splittings over coarse Poincaré duality groups |
| title_sort | quasi isometry invariance of group splittings over coarse poincare duality groups |
| work_keys_str_mv | AT margolisa quasiisometryinvarianceofgroupsplittingsovercoarsepoincaredualitygroups |