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

Clara Franchi, Michel Boileau, Mattia Mecchia, Luisa Paoluzzi, Bruno Zimmermann

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

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.
Original languageEnglish
Pages (from-to)283-308
Number of pages26
JournalJournal of Topology
Volume11
DOIs
Publication statusPublished - 2018

Keywords

  • 3-manifolds
  • cyclic covering of knot
  • finite groups

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