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Journal of Topology Advance Access published online on May 9, 2008
Journal of Topology, doi:10.1112/jtopol/jtn011
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© 2008 London Mathematical Society

On cyclic branched coverings of prime knots

Michel Boileau

Université Paul Sabatier, Laboratoire Emile Picard (UMR 5580 du CNRS), 118 route de Narbonne, 31062 Toulouse cedex 4 France boileau@picard.ups-tlse.fr

Luisa Paoluzzi

Université de Bourgogne, I.M.B. (UMR 5584 du CNRS), B.P. 47 870, 9 av. Alain Savary, 21078 Dijon cedex France paoluzzi@u-bourgogne.fr


  Abstract

We prove that a prime knot K is not determined by its p-fold cyclic branched cover for at most two odd primes p. Moreover, we show that for a given odd prime p, the p-fold cyclic branched cover of a prime knot K is the p-fold cyclic branched cover of at most one more knot K' non-equivalent to K. To prove the main theorem, a result concerning symmetries of knots is also obtained. This latter result can be interpreted as a characterisation of the trivial knot.

Received February 26, 2007.

2000 Mathematics Subject Classification 57M25 (primary), 57M12, 57M50 (secondary)


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