Higher even dimensional Reidemeister torsion for torus knot exteriors

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.