On π-hyperbolic knots and branched coverings

  title={On π-hyperbolic knots and branched coverings},
  author={Luisa Paoluzzi},
We prove that, for any given n > 2, a π-hyperbolic knot is determined by its 2-fold and n-fold cyclic branched coverings. We also prove that a 2π/m-hyperbolic knot which is not determined by its m-fold and n-fold cyclic branched coverings, 2 < m < n, must have genus (n− 1)(m− 1)/2. Mathematics Subject Classification (1991). Primary 57M25; Secondary 57M12.