Hyperbolicity and identification of Berge knots of types VII and VIII

Mathematics – Geometric Topology

Scientific paper

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25 pages, 1 figure, 3 tables

Scientific paper

T. Saito and M. Teragaito asked whether Berge knots of type VII are hyperbolic, and showed that some infinite sequences of the knots are hyperbolic. We show that Berge knots of types VII and VIII are hyperbolic except the known sequence of torus knots. We used the Reidemeister torsions. As a result, the Alexander polynomials of them have already shown their hyperbolicities. We also show that the standard parameters identify Berge knots of types VII and VIII, and study what kind of information identify them.

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