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Mapping class groups of negatively curved four-manifolds

  • Weizhe Niu
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Abstract

For every closed oriented smooth four-manifold M admitting a metric of strictly negative sectional curvature, we prove that dimℚH1(T(M);ℚ)=dimℚH1(TTOP(M);ℚ)=∞ where T(M) and TTOP(M) denote the Torelli groups. This extends a theorem of Budney--Gabai for real hyperbolic manifolds.

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Cite

BibTeXRIS
BibTeX
@misc{niu2026mapping,
  title = {{Mapping class groups of negatively curved four-manifolds}},
  author = {Weizhe Niu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.24562},
  eprint = {2609.24562},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.24562},
}
RIS
TY  - UNPB
TI  - Mapping class groups of negatively curved four-manifolds
AU  - Weizhe Niu
PY  - 2026
DA  - 2026/09/21
PB  - arXiv
DO  - 10.48550/arxiv.2609.24562
UR  - https://arxiv.org/abs/2609.24562
AB  - For every closed oriented smooth four-manifold M admitting a metric of strictly negative sectional curvature, we prove that dim_ℚH_1(T(M);ℚ)=dim_ℚH_1(T_TOP(M);ℚ)=∞ where T(M) and T_TOP(M) denote the Torelli groups. This extends a theorem of Budney--Gabai for real hyperbolic manifolds.
ER  -