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Higher even dimensional Reidemeister torsion for torus knot exteriors

Published online by Cambridge University Press:  25 April 2013

YOSHIKAZU YAMAGUCHI
YOSHIKAZU YAMAGUCHI*
Affiliation:
Department of Mathematics, Akita University1-1 Tegata-Gakuenmachi, Akita, 010-8502, Japan. e-mail: shouji@math.akita-u.ac.jp
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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 1/(2N)2) log | Tor(EK; ρ2N)| converges to zero when N goes to infinity where TorEK; ρ2N is the higher dimensional Reidemeister torsion of a torus knot exterior and an acyclic SL2N(ℂ)-representation of the torus knot group. We also give a classification for SL2(ℂ)-representations of torus knot groups, which induce acyclic SL2N(ℂ)-representations.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 155 , Issue 2 , September 2013 , pp. 297 - 305
Copyright
Copyright © Cambridge Philosophical Society 2013 

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References

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