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Sasakian Manifolds with Perfect Fundamental Groups

Volume 14, Number 2 (2012), 98 - 117

Sasakian Manifolds with Perfect Fundamental Groups

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Abstract

Using the Sasakian join construction with homology 3-spheres, we give a countably infinite number of examples of Sasakian manifolds with perfect fundamental group in all odd dimensions ≥ 3. These have extremal Sasaki metrics with constant scalar curvature. Moreover, we present further examples of both Sasaki-Einstein and Sasaki-η-Einstein metrics.