On cyclic branched coverings of prime knots

Details On cyclic branched coverings of prime knots On cyclic branched coverings of prime knots

2007-02-26

arxiv.org/abs/math/0702783v1

Mathematics

Geometric Topology

28 pages, 2 figures

Scientific paper

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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