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.
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https://hal.archives-ouvertes.fr/hal-00638092
Contributor : Luisa Paoluzzi <>
Submitted on : Thursday, November 3, 2011 - 8:30:02 PM
Last modification on : Monday, April 29, 2019 - 5:20:57 PM

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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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