As a consequence of a general result about finite group actions on 3-manifolds, we show that a hyperbolic 3-manifold can be the cyclic branched cover of at most fifteen inequivalent knots in S3 (in fact, a main motivation of the present paper is to establish the existence of such a universal bound). A similar, though weaker, result holds for arbitrary irreducible 3-manifolds: an irreducible 3-manifold can be a cyclic branched cover of odd prime order of at most six knots in S3. We note that in most other cases such a universal bound does not exist.

Boileau, M., Franchi, C., Mecchia, M., Paoluzzi, L., Zimmermann, B., Finite group actions on 3-manifolds and cyclic branched covers of knots, <<JOURNAL OF TOPOLOGY>>, 2018; 11 (2): 283-308. [doi:10.1112/topo.12052] [http://hdl.handle.net/10807/118954]

Finite group actions on 3-manifolds and cyclic branched covers of knots

Franchi, Clara;
2018

Abstract

As a consequence of a general result about finite group actions on 3-manifolds, we show that a hyperbolic 3-manifold can be the cyclic branched cover of at most fifteen inequivalent knots in S3 (in fact, a main motivation of the present paper is to establish the existence of such a universal bound). A similar, though weaker, result holds for arbitrary irreducible 3-manifolds: an irreducible 3-manifold can be a cyclic branched cover of odd prime order of at most six knots in S3. We note that in most other cases such a universal bound does not exist.
Inglese
Boileau, M., Franchi, C., Mecchia, M., Paoluzzi, L., Zimmermann, B., Finite group actions on 3-manifolds and cyclic branched covers of knots, <<JOURNAL OF TOPOLOGY>>, 2018; 11 (2): 283-308. [doi:10.1112/topo.12052] [http://hdl.handle.net/10807/118954]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10807/118954
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