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<p>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 their singular sets, thereby confirming a conjecture posed by Florit and Ziller. Then we compute the orbifold cohomology rings of those with a specific singular locus. This reveals a distinctive behaviour 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.</p>

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On the geometry and topology of positively curved Eschenburg orbifolds

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月13日

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  • Dennis Wulle,
  • Masoumeh Zarei

摘要

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 their singular sets, thereby confirming a conjecture posed by Florit and Ziller. Then we compute the orbifold cohomology rings of those with a specific singular locus. This reveals a distinctive behaviour 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.