## 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 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.

Original language | English |
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Pages (from-to) | 297-305 |

Number of pages | 9 |

Journal | Mathematical Proceedings of the Cambridge Philosophical Society |

Volume | 155 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2013 Sept |

Externally published | Yes |

## ASJC Scopus subject areas

- Mathematics(all)