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Einstein metrics on rational homology 7-spheres

Charles P. BoyerKrzysztof GalickiMichael Nakamaye — 2002

Annales de l’institut Fourier

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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