A Survey on Simplicial Volume and Invariants of Foliations and Laminations

Kuessner, Thilo

doi:10.1142/9789812772640_0015

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Simplicial Volume1

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Cited by 2 publications

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“…Recall that the proportionality principle of simplicial volume for open manifolds fails in general. It is known, however, that the proportionality principle for R-rank 1 locally symmetric spaces holds ( [6]). Now, we establish the proportionality principle for connected, complete, pinched negatively curved manifolds of finite volume by Theorems 3.2 and 3.4, which generalizes the proportionality principle for R-rank 1 locally symmetric spaces.…”

Section: Simplicial Volumementioning

confidence: 99%

Simplicial volume of compact manifolds with amenable boundary

Kim

Kuessner

2014

J. Topol. Anal.

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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.

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Section: Simplicial Volumementioning

confidence: 99%