Degree theorems and Lipschitz simplicial volume for non-positively curved manifolds of finite volume

Clara Loeh; Roman Sauer

doi:10.1112/jtopol/jtp005

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arXiv · 0710.1635

Degree theorems and Lipschitz simplicial volume for non-positively curved manifolds of finite volume

Clara Loeh·Roman Sauer

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Abstract

We study a metric version of the simplicial volume on Riemannian manifolds, the Lipschitz simplicial volume, with applications to degree theorems in mind. We establish a proportionality principle and a product inequality from which we derive an extension of Gromov's volume comparison theorem to products of negatively curved manifolds or locally symmetric spaces of non-compact type. In contrast, we provide vanishing results for the ordinary simplicial volume; for instance, we show that the ordinary simplicial volume of non-compact locally symmetric spaces with finite volume of Q-rank at least 3 is zero.

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Clara Loeh, Roman Sauer. 2009-01-30. Degree theorems and Lipschitz simplicial volume for non-positively curved manifolds of finite volume. https://doi.org/10.1112/jtopol%2Fjtp005

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