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Einstein Metrics on Rational Homology 7-Spheres

Charles P. Boyer·Krzysztof Galicki·Michael Nakamaye
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Abstract

In this paper we demonstrate the existence of Sasakian-Einstein structures on certain 2-connected rational homology 7-spheres. These appear to be the first non-regular examples of Sasakian-Einstein metrics on simply connected rational homology spheres. We also briefly describe the rational homology 7-spheres that admit regular positive Sasakian structures.

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Charles P. Boyer, Krzysztof Galicki, Michael Nakamaye. 2001-08-16. Einstein Metrics on Rational Homology 7-Spheres. https://arxiv.org/abs/math/0108113

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