English

Higher even dimensional Reidemeister torsion for torus knot exteriors

Geometric Topology 2013-02-27 v3 Algebraic Topology

Abstract

We study the asymptotics of the higher dimensional Reidemeister torsion for torus knot exteriors, which is related to the results by W. M\"uller 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.

Keywords

Cite

@article{arxiv.1208.4452,
  title  = {Higher even dimensional Reidemeister torsion for torus knot exteriors},
  author = {Yoshikazu Yamaguchi},
  journal= {arXiv preprint arXiv:1208.4452},
  year   = {2013}
}

Comments

9 pages, 1 figure; V2:Exposition improved; V3: Typos corrected, references updated, to appear in Mathematical Proceedings of the Cambridge Philosophical Society