A Topological Splitting Theorem for Poincare Duality Groups and High-dimensional Manifolds
We show that for a wide class of manifold pairs N, M satisfying dim(M) = dim(N) + 1, every \pi_1-injective map f : N --> M factorises up to homotopy as a finite cover of an embedding. This result, in the spirit of Waldhausen's torus theorem, is derived using Cappell's surgery method...
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| Format: | Journal article |
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2011
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| _version_ | 1826266950787923968 |
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| author | Kar, A Niblo, G |
| author_facet | Kar, A Niblo, G |
| author_sort | Kar, A |
| collection | OXFORD |
| description | We show that for a wide class of manifold pairs N, M satisfying dim(M) = dim(N) + 1, every \pi_1-injective map f : N --> M factorises up to homotopy as a finite cover of an embedding. This result, in the spirit of Waldhausen's torus theorem, is derived using Cappell's surgery methods from a new algebraic splitting theorem for Poincare duality groups. As an application we derive a new obstruction to the existence of \pi_1-injective maps. |
| first_indexed | 2024-03-06T20:46:44Z |
| format | Journal article |
| id | oxford-uuid:3629b7e4-14f1-4914-9b2f-f8820efe4eb2 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T20:46:44Z |
| publishDate | 2011 |
| record_format | dspace |
| spelling | oxford-uuid:3629b7e4-14f1-4914-9b2f-f8820efe4eb22022-03-26T13:36:09ZA Topological Splitting Theorem for Poincare Duality Groups and High-dimensional ManifoldsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:3629b7e4-14f1-4914-9b2f-f8820efe4eb2Symplectic Elements at Oxford2011Kar, ANiblo, GWe show that for a wide class of manifold pairs N, M satisfying dim(M) = dim(N) + 1, every \pi_1-injective map f : N --> M factorises up to homotopy as a finite cover of an embedding. This result, in the spirit of Waldhausen's torus theorem, is derived using Cappell's surgery methods from a new algebraic splitting theorem for Poincare duality groups. As an application we derive a new obstruction to the existence of \pi_1-injective maps. |
| spellingShingle | Kar, A Niblo, G A Topological Splitting Theorem for Poincare Duality Groups and High-dimensional Manifolds |
| title | A Topological Splitting Theorem for Poincare Duality Groups and
High-dimensional Manifolds |
| title_full | A Topological Splitting Theorem for Poincare Duality Groups and
High-dimensional Manifolds |
| title_fullStr | A Topological Splitting Theorem for Poincare Duality Groups and
High-dimensional Manifolds |
| title_full_unstemmed | A Topological Splitting Theorem for Poincare Duality Groups and
High-dimensional Manifolds |
| title_short | A Topological Splitting Theorem for Poincare Duality Groups and
High-dimensional Manifolds |
| title_sort | topological splitting theorem for poincare duality groups and high dimensional manifolds |
| work_keys_str_mv | AT kara atopologicalsplittingtheoremforpoincaredualitygroupsandhighdimensionalmanifolds AT niblog atopologicalsplittingtheoremforpoincaredualitygroupsandhighdimensionalmanifolds AT kara topologicalsplittingtheoremforpoincaredualitygroupsandhighdimensionalmanifolds AT niblog topologicalsplittingtheoremforpoincaredualitygroupsandhighdimensionalmanifolds |