2024/09/27 by Wulle, Dennis, Zarei, Masoumeh
#53C21 #53C25 #57R18 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.2409.19105
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.