Stallings's fibring theorem and PD3-pairs
We give a relatively self-contained proof that if G fibres algebraically and is part of a PD3-pair, then G is the fundamental group of a fibred compact aspherical 3-manifold. This yields a homological proof of a classical theorem of Stallings: if G = π1(M3) is the fundamental group of a compact irre...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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American Mathematical Society
2024
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| _version_ | 1811139226579763200 |
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| author | Bridson, MR Kielak, D Kudlinska, M |
| author_facet | Bridson, MR Kielak, D Kudlinska, M |
| author_sort | Bridson, MR |
| collection | OXFORD |
| description | We give a relatively self-contained proof that if G fibres algebraically and is part of a PD3-pair, then G is the fundamental group of a fibred compact aspherical 3-manifold. This yields a homological proof of a classical theorem of Stallings: if G = π1(M3) is the fundamental group of a compact irreducible 3-manifold M3 and ϕ: G → Z is a surjective homomorphism with finitely generated kernel, then ϕ is induced by a topological fibration of M3 over the circle. |
| first_indexed | 2024-04-09T03:58:39Z |
| format | Journal article |
| id | oxford-uuid:eb417ae0-ef42-4344-92f8-e4797cd30851 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-09-25T04:02:43Z |
| publishDate | 2024 |
| publisher | American Mathematical Society |
| record_format | dspace |
| spelling | oxford-uuid:eb417ae0-ef42-4344-92f8-e4797cd308512024-05-02T09:18:52ZStallings's fibring theorem and PD3-pairsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:eb417ae0-ef42-4344-92f8-e4797cd30851EnglishSymplectic ElementsAmerican Mathematical Society2024Bridson, MRKielak, DKudlinska, MWe give a relatively self-contained proof that if G fibres algebraically and is part of a PD3-pair, then G is the fundamental group of a fibred compact aspherical 3-manifold. This yields a homological proof of a classical theorem of Stallings: if G = π1(M3) is the fundamental group of a compact irreducible 3-manifold M3 and ϕ: G → Z is a surjective homomorphism with finitely generated kernel, then ϕ is induced by a topological fibration of M3 over the circle. |
| spellingShingle | Bridson, MR Kielak, D Kudlinska, M Stallings's fibring theorem and PD3-pairs |
| title | Stallings's fibring theorem and PD3-pairs |
| title_full | Stallings's fibring theorem and PD3-pairs |
| title_fullStr | Stallings's fibring theorem and PD3-pairs |
| title_full_unstemmed | Stallings's fibring theorem and PD3-pairs |
| title_short | Stallings's fibring theorem and PD3-pairs |
| title_sort | stallings s fibring theorem and pd3 pairs |
| work_keys_str_mv | AT bridsonmr stallingssfibringtheoremandpd3pairs AT kielakd stallingssfibringtheoremandpd3pairs AT kudlinskam stallingssfibringtheoremandpd3pairs |