English

On cyclic branched coverings of prime knots

Geometric Topology 2014-02-26 v1

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.

Keywords

Cite

@article{arxiv.math/0702783,
  title  = {On cyclic branched coverings of prime knots},
  author = {M. Boileau and L. Paoluzzi},
  journal= {arXiv preprint arXiv:math/0702783},
  year   = {2014}
}

Comments

28 pages, 2 figures