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 ; ρ 2N)| converges to zero when N goes to infinity where TorEK ; ρ 2N is the higher dimensional Reidemeister torsion of a torus knot exterior and an acyclic SL 2N(â.,)-representation of the torus knot group. We also give a classification for SL 2(â.,)- representations of torus knot groups, which induce acyclic SL 2N(â.,)-representations.
|Number of pages||9|
|Journal||Mathematical Proceedings of the Cambridge Philosophical Society|
|Publication status||Published - 2013 Sept|
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