L2-torsion of Hyperbolic Manifolds of Finite Volume
1999 | journal article
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- Authors
- Lück, W. ; Schick, T.
- Abstract
- Suppose M¯ is a compact connected odd-dimensional manifold with boundary, whose interior M comes with a complete hyperbolic metric of finite volume. We will show that the L2-topological torsion of M¯ and the L2-analytic torsion of the Riemannian manifold M are equal. In particular, the L2-topological torsion of M¯ is proportional to the hyperbolic volume of M, with a constant of proportionality which depends only on the dimension and which is known to be nonzero in odd dimensions [HS]. In dimension 3 this proves the conjecture [Lü2, Conjecture 2.3] or [LLü, Conjecture 7.7] which gives a complete calculation of the L2-topological torsion of compact L2-acyclic 3-manifolds which admit a geometric JSJT-decomposition.¶In an appendix we give a counterexample to an extension of the Cheeger-Müller theorem to manifolds with boundary: if the metric is not a product near the boundary, in general analytic and topological torsion are not equal, even if the Euler characteristic of the boundary vanishes.
- Issue Date
- 1999
- Journal
- Geometric and Functional Analysis
- ISSN
- 1016-443X
- Language
- English