Simplicial volume of fiber bundles with nonpositively curved fibers

Xiaofeng Meng

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arXiv · 2111.06165

Simplicial volume of fiber bundles with nonpositively curved fibers

Xiaofeng Meng

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Abstract

We prove the simplicial volume of the total space of a smooth fiber bundle with fiber being an oriented closed connected (occ) manifold of nonpositive curvature and negative Ricci curvature over an occ manifold with a closed universal covering is zero. Furthermore, if the fiber is an occ negatively curved manifold with dimension more than $2$, the simplicial volume of the total space is zero if and only if the simplicial volume of the base space is zero.

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Xiaofeng Meng. 2021-11-11. Simplicial volume of fiber bundles with nonpositively curved fibers. https://arxiv.org/abs/2111.06165

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