On the Geometry and Topology of Positively Curved Eschenburg Orbifolds
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916413715775488 |
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| author | Wulle, Dennis Zarei, Masoumeh |
| author_facet | Wulle, Dennis Zarei, Masoumeh |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_19105 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Geometry and Topology of Positively Curved Eschenburg Orbifolds Wulle, Dennis Zarei, Masoumeh Differential Geometry Geometric Topology 53C21, 53C25, 57R18 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. |
| title | On the Geometry and Topology of Positively Curved Eschenburg Orbifolds |
| topic | Differential Geometry Geometric Topology 53C21, 53C25, 57R18 |
| url | https://arxiv.org/abs/2409.19105 |