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...
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Format: | Journal article |
Language: | English |
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American Mathematical Society
2024
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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 |