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Article Dans Une Revue Journal of topology Année : 2018

Finite group actions and cyclic branched covers of knots in $\mathbf{S}^3$

Résumé

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 $\mathbf{S}^3$.
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Dates et versions

hal-01160794 , version 1 (05-07-2023)

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Michel Boileau, Clara Franchi, Mattia Mecchia, Luisa Paoluzzi, Bruno Zimmermann. Finite group actions and cyclic branched covers of knots in $\mathbf{S}^3$. Journal of topology, 2018, 11 (2), pp.283-308. ⟨10.1112/topo.12052⟩. ⟨hal-01160794⟩
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