Higher dimensional Reidemeister torsion invariants for cusped hyperbolic 3-manifoldsReport as inadecuate



 Higher dimensional Reidemeister torsion invariants for cusped hyperbolic 3-manifolds


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For an oriented finite volume hyperbolic 3-manifold M with a fixed spin structure \eta, we consider a sequence of invariants {\tau n(M; \eta)}. Roughly speaking, {\tau n(M; \eta)} is the Reidemeister torsion of M with respect to the representation given by the composition of the lift of the holonomy representation defined by \eta, 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 behavior and its relationship with the complex-length spectrum of the manifold. Concerning the former, we prove that for suitable spin structures, log(\tau n(M; \eta)) grows as -n^2 Vol(M)-4\pi, extending thus the result obtained by W. Mueller for the compact case. Concerning the latter, we prove that the sequence {\tau n(M; \eta)} determines the complex-length spectrum of the manifold up to complex conjugation.



Author: Pere Menal-Ferrer; Joan Porti

Source: https://archive.org/







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