Hyperbolicity and identification of Berge knots of types VII and VIII

2011/07/02 by Teruhisa Kadokami, Kadokami, Teruhisa
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #math.GT

paper · pdf · doi:10.48550/arxiv.1107.0379

25 pages, 1 figure, 3 tables

arxiv created 2012/04/02 · arxiv updated 2012/04/03

Abstract

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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