Simplicial volume of compact manifolds with amenable boundary

2012/05/07 by Kim, Sungwoon, Kuessner, Thilo · 1 citation
#53C23 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1205.1375

Abstract

Let M be the interior of a connected, oriented, compact manifold V of dimension at least 2. If each path component of ∂ V has amenable fundamental group, then we prove that the simplicial volume of M is equal to the relative simplicial volume of V and also to the geometric (Lipschitz) simplicial volume of any Riemannian metric on M whenever the latter is finite. As an application we establish the proportionality principle for the simplicial volume of complete, pinched negatively curved manifolds of finite volume.

Cited by

• On measure homology of mildly wild spaces

Related

• The Proportionality Principle of Simplicial Volume
• Piecewise straightening and Lipschitz simplicial volume
• Topological volumes of certain complete affine manifolds
• Simplicial volume and 0-strata of separating filtrations
• The spectrum of simplicial volume of non-compact manifolds