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Peer-reviewedCC BY-SA 4.0Symmetry, Integrability and Geometry: Methods and Applications

Free Circle Actions and Positive Ricci Curvature on Manifolds with the Cohomology Ring of S2× S5

  • Philipp Reiser1
  1. 1Karlsruhe, Germany
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Abstract

We classify which of the 672 oriented diffeomorphism types of closed, simply-connected spin 7-manifolds with the cohomology ring of S2× S5 admit a free circle action. In addition, we show that whenever such an action exists, there exist infinitely many pairwise non-equivalent free circle actions. Finally, in almost all cases where such an action exists, we construct invariant Riemannian metrics of positive Ricci curvature.

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Cite

BibTeXRIS
BibTeX
@article{reiser2026free,
  title = {{Free Circle Actions and Positive Ricci Curvature on Manifolds with the Cohomology Ring of $S^2\times S^5$}},
  author = {Philipp Reiser},
  journal = {Symmetry, Integrability and Geometry: Methods and Applications},
  year = {2026},
  month = oct,
  doi = {10.3842/sigma.2026.094},
  url = {https://sigma-journal.com/2026/094/},
  note = {CC BY-SA 4.0},
}
RIS
TY  - JOUR
TI  - Free Circle Actions and Positive Ricci Curvature on Manifolds with the Cohomology Ring of S^2× S^5
AU  - Philipp Reiser
PY  - 2026
DA  - 2026/10/02
JO  - Symmetry, Integrability and Geometry: Methods and Applications
DO  - 10.3842/sigma.2026.094
UR  - https://sigma-journal.com/2026/094/
AB  - We classify which of the 672 oriented diffeomorphism types of closed, simply-connected spin 7-manifolds with the cohomology ring of S^2× S^5 admit a free circle action. In addition, we show that whenever such an action exists, there exist infinitely many pairwise non-equivalent free circle actions. Finally, in almost all cases where such an action exists, we construct invariant Riemannian metrics of positive Ricci curvature.
SN  - 1815-0659
ER  -