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Journal Articles J. Topol. Year : 2008

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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Dates and versions

hal-00638092 , version 1 (03-11-2011)

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  • HAL Id : hal-00638092 , version 1

Cite

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