The asymptotics of the Ray-Singer analytic torsion of hyperbolic 3-manifolds
Abstract
In this paper we consider the analytic torsion of a closed hyperbolic 3-manifold associated with the m-th symmetric power of the standard representation of SL(2,C) and we study its asymptotic behavior if m tends 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.
- Publication:
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arXiv e-prints
- Pub Date:
- March 2010
- DOI:
- 10.48550/arXiv.1003.5168
- arXiv:
- arXiv:1003.5168
- Bibcode:
- 2010arXiv1003.5168M
- Keywords:
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- Mathematics - Spectral Theory;
- Mathematics - Representation Theory;
- Primary: 58J52;
- Secondary: 11M36
- E-Print:
- 35 pages