On pi-hyperbolic knots and branched coverings

Luisa Paoluzzi (1)

1 LEP - Laboratoire Émile Picard

We prove that, for any given n > 2, a pi-hyperbolic knot is determined by its 2-fold and n-fold cyclic branched coverings. We also prove that a 2pi/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.

Domaines: Topologie géométrique [math.GT]

Luisa Paoluzzi. On pi-hyperbolic knots and branched coverings. Comment. Math. Helv., 1999, 74, pp.467-475. ⟨hal-00638124⟩