Efficient fundamental cycles of cusped hyperbolic manifolds

2000/07/01 by Kuessner, Thilo
#57M50 #57R30 #FOS: Mathematics #Geometric Topology (math.GT) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.math/0007003

Abstract

Let N be a manifold (with boundary) of dimension at least 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. 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.

Related

• A quantitative version of a theorem by Jungreis
• Notes on the peripheral volume of hyperbolic 3-manifolds
• Volume and structure of hyperbolic 3-manifolds
• New bounds for the simplicial volume of complex hyperbolic surfaces
• Simple closed geodesics in cusped hyperbolic 3-manifolds