Three cyclic branched covers suffice to determine hyperbolic knots.

Luisa Paoluzzi (1)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]

Let n > m > 2 be two fixed coprime integers. We prove that two Conway reducible, hyperbolic knots sharing the 2-fold, m-fold and n-fold cyclic branched covers are equivalent. Using previous results by Zimmermann we prove that this implies that a hyperbolic knot is determined by any three of its cyclic branched covers.

Domaines: Topologie géométrique [math.GT]

Luisa Paoluzzi. Three cyclic branched covers suffice to determine hyperbolic knots.. J. Knot Theory Ramifications, 2005, 14, pp.641-655. ⟨hal-00638120⟩