Simply connected Sasaki-Einstein rational homology 5-spheres
Jihun Park, Joonyeong Won
TL;DR
This paper classifies all simply connected rational homology 5-spheres that can support Sasaki-Einstein metrics, providing a complete characterization in this geometric context.
Contribution
It offers a complete classification of simply connected rational homology 5-spheres admitting Sasaki-Einstein metrics, filling a gap in geometric topology and differential geometry.
Findings
Identifies all such 5-spheres that admit Sasaki-Einstein metrics
Provides explicit criteria for the existence of these metrics
Completes the classification problem for this class of manifolds
Abstract
We completely determine which simply connected rational homology 5-spheres admit Sasaki-Einstein metrics.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Algebraic Geometry and Number Theory