Higher even dimensional Reidemeister torsion for torus knot exteriors
arXiv:1208.4452
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.
9 pages, 1 figure; V2:Exposition improved; V3: Typos corrected, references updated, to appear in Mathematical Proceedings of the Cambridge Philosophical Society