Higher-dimensional Reidemeister torsion invariants for cusped hyperbolic 3-manifolds

Pere Menal-Ferrer, Joan Porti

Research output: Contribution to journalArticleResearchpeer-review

20 Citations (Scopus)

Abstract

For an oriented finite volume hyperbolic 3-manifold M with a fixed spin structure η, we consider a sequence of invariants {Τn(M; η)}. Roughly speaking, Τn(M; η) is the Reidemeister torsion of M with respect to the representation given by the composition of the lift of the holonomy representation defined by η, and the n-dimensional, irreducible, complex representation of SL(2, C). In the present work, we focus on two aspects of this invariant: its asymptotic behaviour and its relationship with the complex-length spectrum of the manifold. Concerning the former, we prove that, for suitable spin structures, log |Τn(M; η)| ̃-n2 (Vol M/4π), extending thus the result obtained by Müller for the compact case. Concerning the latter, we prove that the sequence {|Τn(M; η)|} determines the complex-length spectrum of the manifold up to complex conjugation. © 2013 London Mathematical Society.
Original languageEnglish
Article numberjtt024
Pages (from-to)69-119
JournalJournal of Topology
Volume7
Issue number1
DOIs
Publication statusPublished - 1 Jan 2014

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