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PreprintarXiv licencearXiv

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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Cite

BibTeXRIS
BibTeX
@misc{ma2026gromovs,
  title = {{Gromov's Simplicial Volume Vanishing Conjecture for Positive Scalar Curvature}},
  author = {Qiaochu Ma and Jinmin Wang and Zhizhang Xie and Guoliang Yu and Bo Zhu},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2606.29135},
  eprint = {2606.29135},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.29135},
}
RIS
TY  - UNPB
TI  - Gromov's Simplicial Volume Vanishing Conjecture for Positive Scalar Curvature
AU  - Qiaochu Ma
AU  - Jinmin Wang
AU  - Zhizhang Xie
AU  - Guoliang Yu
AU  - Bo Zhu
PY  - 2026
DA  - 2026/08/28
PB  - arXiv
DO  - 10.48550/arxiv.2606.29135
UR  - https://arxiv.org/abs/2606.29135
AB  - 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.
ER  -