On cyclic branched coverings of prime knots

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' 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.
Type de document :
Article dans une revue
J. Topol., 2008, 1, pp.557-583
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https://hal.archives-ouvertes.fr/hal-00638092
Contributeur : Luisa Paoluzzi <>
Soumis le : jeudi 3 novembre 2011 - 20:30:02
Dernière modification le : mardi 11 septembre 2018 - 15:18:14

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  • HAL Id : hal-00638092, version 1

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Michel Boileau, Luisa Paoluzzi. On cyclic branched coverings of prime knots. J. Topol., 2008, 1, pp.557-583. 〈hal-00638092〉

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