Einstein Metrics on Rational Homology Spheres
Charles P. Boyer, Krzysztof Galicki
TL;DR
This paper demonstrates the existence of Sasakian-Einstein metrics on infinitely many rational homology spheres across all odd dimensions greater than 3, with sharper results in dimension 5 and exponential growth in parameters.
Contribution
It proves the existence of Sasakian-Einstein metrics on infinitely many rational homology spheres in all odd dimensions greater than 3, including sharper results in dimension 5.
Findings
Existence of Sasakian-Einstein metrics on infinitely many rational homology spheres
Sharper results obtained in dimension 5
Number of effective parameters grows exponentially with dimension
Abstract
We prove the existence of Sasakian-Einstein metrics on infinitely many rational homology spheres in all odd dimensions greater than 3. In dimension 5 we obain somewhat sharper results. There are examples where the number of effective parameters in the Einstein metric grows exponentially with dimension.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Algebraic Geometry and Number Theory