L^2-torsion of hyperbolic manifolds of finite volume

Details L^2-torsion of hyperbolic manifolds of finite volume L^2-torsion of hyperbolic manifolds of finite volume

1997-07-10

arxiv.org/abs/dg-ga/9707009v2

Geom. Funct. Anal. 9 (1999), no. 3, 518--567

Mathematics

Differential Geometry

42 pages, AMS-Latex2e V2: identical with published version, in particular including an additional appendix with examples for n

Scientific paper

Suppose $\bar{M}$ 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 $L^2$-topological torsion of $\bar{M}$ and the $L^2$-analytic torsion of the Riemannian manifold $M$ are equal. In particular, the $L^2$-topological torsion of $\bar{M}$ 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 dimension 3, 5 and 7. In dimension 3 this proves the conjecture Of Lott and Lueck which gives a complete calculation of the $L^2$-topological torsion of compact $L^2$-acyclic 3-manifolds which admit a geometric torus-decomposition. In an appendix we give a counterexample to an extension of the Cheeger-Mueller 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. Keywords: L^2-torsion, hyperbolic manifolds, 3-manifolds

Affiliated with

Also associated with

No associations

Rating

L^2-torsion of hyperbolic manifolds of finite volume does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with L^2-torsion of hyperbolic manifolds of finite volume, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and L^2-torsion of hyperbolic manifolds of finite volume will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-399290