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arXiv · 1208.4452

Higher even dimensional Reidemeister torsion for torus knot exteriors

Yoshikazu Yamaguchi
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Abstract

We study the asymptotics of the higher dimensional Reidemeister torsion for torus knot exteriors, which is related to the results by W. Müller and P. Menal-Ferrer and J. Porti on the asymptotics of the Reidemeister torsion and the hyperbolic volumes for hyperbolic 3-manifolds. We show that the sequence of log |the higher dimensional Reidemeister torsion of a torus knot exterior with SL(2N,C)-representation| / (2N)^2 converges to zero when N goes to infinity. We also give a classification for SL(2,C)-representations of torus knot groups, which induce acyclic SL(2N,C)-representations.

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Yoshikazu Yamaguchi. 2013-02-26. Higher even dimensional Reidemeister torsion for torus knot exteriors. https://arxiv.org/abs/1208.4452

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