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

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.

33 pages; corrected the vanishing result (and adapted Section 5 accordingly), minor expository changes in the introduction

References in corpus (1)

• The simplicial volume of closed manifolds covered by H^2 x H^2

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• Smith theory, L2 cohomology, isometries of locally symmetric manifolds and moduli spaces of curves
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