On π \pi -hyperbolic knots and branched coverings

  • L. Paoluzzi

    Université Paul Sabatier, Toulouse, France


We prove that, for any given n>2n > 2 , a π\pi -hyperbolic knot is determined by its 2-fold and n-fold cyclic branched coverings. We also prove that a 2π/m2\pi/m -hyperbolic knot which is not determined by its m-fold and n-fold cyclic branched coverings, 2<m<n2 < m < n , must have genus (n1)(m1)/2(n - 1)(m - 1)/2 .

Cite this article

L. Paoluzzi, On π \pi -hyperbolic knots and branched coverings. Comment. Math. Helv. 74 (1999), no. 3, pp. 467–475

DOI 10.1007/S000140050100