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arXiv · 2409.19105

On the Geometry and Topology of Positively Curved Eschenburg Orbifolds

Dennis Wulle·Masoumeh Zarei
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Abstract

The present article explores the relationship between positive sectional curvature and the geometric and topological properties of Eschenburg $6$-orbifolds. First, we prove that positive sectional curvature imposes restrictions on the their singular sets, thereby confirming a conjecture posed by Florit and Ziller. Then we compute the orbifold cohomology rings for those with a specific singular locus. This reveals a distinctive behavior in the cohomology groups of positively curved Eschenburg orbifolds compared to their non-negatively curved counterparts. Furthermore, we compute the orbifold cohomology rings of all Eschenburg orbifolds.

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Dennis Wulle, Masoumeh Zarei. 2024-09-27. On the Geometry and Topology of Positively Curved Eschenburg Orbifolds. https://arxiv.org/abs/2409.19105

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