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.
2018
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]
File in questo prodotto:
File Dimensione Formato  
FGAstampa.pdf

non disponibili

Tipologia file ?: Versione Editoriale (PDF)
Licenza: Non specificato
Dimensione 92.88 kB
Formato Unknown
92.88 kB Unknown   Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10807/118954
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 1
social impact