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Journal of Topology Advance Access originally published online on May 9, 2008
Journal of Topology 2008 1(3):557-583; 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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