Lück W. and Schick, T.: L2-torsion of hyperbolic manifolds of finite volume
Abstract: Suppose $overline{M}$ 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
$overline{M}$ and the $L^2$-analytic torsion
of the Riemannian manifold $M$ are equal.
In particular, the $L^2$-topological torsion of
$overline{M}$ is proportional to the
hyperbolic volume of $M$, with a constant of
proportionality which depends only on the
dimension and which is nonzero in
odd dimension. In dimension 3 this proves
a 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 JSJT-decomposition.\[2mm]
Key words: $L^2$-torsion, hyperbolic manifolds, $3$-manifolds\
AMS-classification number: 58G11
Thomas Schick