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arXiv · 2606.29135

Gromov's Simplicial Volume Vanishing Conjecture for Positive Scalar Curvature

Qiaochu Ma·Jinmin Wang·Zhizhang Xie·Guoliang Yu·Bo Zhu
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Abstract

In this paper, we prove Gromov's simplicial volume vanishing conjecture for closed manifolds with spin universal cover. More precisely, we show that if a closed oriented manifold admits a metric of nonnegative scalar curvature and its universal cover is spin, then its simplicial volume vanishes. In particular, a closed oriented aspherical manifold with nonzero simplicial volume admits no metric of nonnegative scalar curvature.

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Qiaochu Ma, Jinmin Wang, Zhizhang Xie, Guoliang Yu, Bo Zhu. 2026-06-28. Gromov's Simplicial Volume Vanishing Conjecture for Positive Scalar Curvature. https://arxiv.org/abs/2606.29135

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