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Commentarii Mathematici Helvetici

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Volume 94, Issue 3, 2019, pp. 459–531
DOI: 10.4171/CMH/466

Published online: 2019-09-25

Asymptotics of analytic torsion for hyperbolic three-manifolds

Jean Raimbault[1]

(1) Université de Toulouse, France

We prove that for certain sequences of hyperbolic three-manifolds with cusps which converge to hyperbolic three-space in a weak (“Benjamini–Schramm”) sense and certain coefficient systems the regularised analytic torsion approximates the $L^2$-torsion of the universal cover.

We also prove an asymptotic equality between the former and the Reidemeister torsion of the truncated manifolds.

Keywords: Analytic torsion, hyperbolic manifolds with cusps, Selberg trace formula

Raimbault Jean: Asymptotics of analytic torsion for hyperbolic three-manifolds. Comment. Math. Helv. 94 (2019), 459-531. doi: 10.4171/CMH/466