Higher even dimensional Reidemeister torsion for torus knot exteriors

2012/08/22 by Yamaguchi, Yoshikazu
#57M05 (Primary) 57M25 (Secondary) #57M27 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/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.

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