The asymptotics of the RaySinger analytic torsion of hyperbolic 3manifolds
Abstract
In this paper we consider the analytic torsion of a closed hyperbolic 3manifold associated with the mth 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 3manifold. It follows that the Reidemeister torsion associated with the symmetric powers determines the volume of a closed hyperbolic 3manifold.
 Publication:

arXiv eprints
 Pub Date:
 March 2010
 DOI:
 10.48550/arXiv.1003.5168
 arXiv:
 arXiv:1003.5168
 Bibcode:
 2010arXiv1003.5168M
 Keywords:

 Mathematics  Spectral Theory;
 Mathematics  Representation Theory;
 Primary: 58J52;
 Secondary: 11M36
 EPrint:
 35 pages