On $ \pi $-hyperbolic knots and branched coverings

L. Paoluzzi

doi:10.1007/s000140050100

JournalscmhVol. 74, No. 3pp. 467–475

On $π$ -hyperbolic knots and branched coverings

L. Paoluzzi
Université Paul Sabatier, Toulouse, France

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

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Abstract

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

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Cite this article

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

DOI 10.1007/S000140050100