# On $\pi$-hyperbolic knots and branched coverings

### L. Paoluzzi

Université Paul Sabatier, Toulouse, France

## Abstract

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 $2\pi/m$ -hyperbolic knot which is not determined by its m-fold and n-fold cyclic branched coverings, $2 < m < n$ , must have genus $(n - 1)(m - 1)/2$ .

## Cite this article

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

DOI 10.1007/S000140050100