|On cyclic branched coverings of prime knots |
Auteur(s): Boileau Michel, Paoluzzi Luisa
(Article) Publié: -J. Topol., vol. 1 p.557-583 (2008)
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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' nonequivalent 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.