Efficient fundamental cycles of cusped hyperbolic manifolds

Thilo Kuessner

Vol. 211 (2003), No. 2, 283–313

DOI: 10.2140/pjm.2003.211.283

Abstract

Let M be a manifold (with boundary) of dimension ≥ 3, such that its interior admits a hyperbolic metric of finite volume. We discuss the possible limits arising from sequences of relative fundamental cycles approximating the simplicial volume ∥M,∂M∥, using ergodic theory of unipotent actions. As applications, we extend results of Jungreis and Calegari from closed hyperbolic to finite-volume hyperbolic manifolds:

a) Strict subadditivity of simplicial volume with respect to isometric glueing along geodesic surfaces, and

b) nontriviality of the foliated Gromov norm for “most” foliations with two-sided branching.

Milestones

Received: 19 April 2002

Revised: 14 December 2002

Published: 1 October 2003