Einstein Metrics on Rational Homology Spheres
classification
🧮 math.DG
hep-thmath.AG
keywords
dimensioneinsteinhomologymetricsrationalspheresdimensionseffective
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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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