Finite group actions and cyclic branched covers of knots in $\mathbf{S}^3$
| Autor: | Boileau, Michel, Franchi, Clara, Mecchia, Mattia, Paoluzzi, Luisa, Zimmermann, Bruno |
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| Přispěvatelé: | Institut de Mathématiques de Marseille (I2M), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), Università cattolica del Sacro Cuore [Brescia] (Unicatt), Università degli studi di Trieste = University of Trieste, Università degli studi di Trieste |
| Jazyk: | angličtina |
| Rok vydání: | 2023 |
| Předmět: |
Mathematics - Geometric Topology
Primary 57S17 Secondary 57M40 57M60 57M12 57M25 57M50 [MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT] FOS: Mathematics Geometric Topology (math.GT) Group Theory (math.GR) Mathematics - Group Theory Mathematics::Symplectic Geometry Mathematics::Geometric Topology [MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR] |
| Zdroj: | Journal of topology Journal of topology, Oxford University Press, 2018, 11 (283-308), ⟨10.1112/topo.12052⟩ |
| ISSN: | 1753-8424 1753-8416 |
| DOI: | 10.1112/topo.12052⟩ |
| Popis: | We show that a hyperbolic $3$-manifold can be the cyclic branched cover of at most fifteen knots in $\mathbf{S}^3$. This is a consequence of a general result about finite groups of orientation preserving diffeomorphisms acting on $3$-manifolds. A similar, although weaker, result holds for arbitrary irreducible $3$-manifolds: an irreducible $3$-manifold can be the cyclic branched cover of odd prime order of at most six knots in $\mathbf{S}^3$. 31 pages, 1 figure. Changes from v2: The paper has been substantially reorganized, in particular the proof of Theorem 2 was considerably shortened. Accepted for publication by the Journal of Topology |
| Databáze: | OpenAIRE |
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