On cyclic branched coverings of prime knots

M. Boileau; L. Paoluzzi

doi:10.1112/jtopol/jtn011

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On cyclic branched coverings of prime knots

M. Boileau·L. Paoluzzi

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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 the symmetries of knots is also obtained. This latter result can be interpreted as a characterisation of the trivial knot.

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BibTeX RIS

M. Boileau, L. Paoluzzi. 2007-02-26. On cyclic branched coverings of prime knots. https://doi.org/10.1112/jtopol%2Fjtn011

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