The Asymptotics of the Ray-Singer Analytic Torsion of Hyperbolic 3-manifolds

By Werner Mueller. 2010

79 citations recorded by the source corpus.

In this paper we consider the analytic torsion of a closed hyperbolic 3-manifold associated with the mth symmetric power of the standard representation of SL(2C) and we study its asymptotic behavior as mtends to infinity. The leading coefficient of the asymptotic formula is given by the volume of the hyperbolic 3-manifold. It follows that the Reidemeister torsion associated with the symmetric powers determines the volume of a closed hyperbolic 3-manifold.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3340ce08c1676a8d93899f7c59f7ed0bf86277c9

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In Applied Mathematics

1. J. Porti
2. P. Menal-Ferrer

In Geometry and Topology

1. J. Porti
2. P. Menal-Ferrer
3. B. Leeb
4. Michael Kapovich
5. Anna Wienhard

In Mathematical Physics

1. J. Porti
2. P. Menal-Ferrer
3. B. Leeb
4. Michael Kapovich
5. Anna Wienhard

Citations in the corpus

• Higher‐dimensional Reidemeister torsion invariants for cusped hyperbolic 3‐manifolds (2011, methodology): “For M compact, this result was established by Müller [25].”