Sasakian Manifolds with Perfect Fundamental Groups

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 $\geq 3$. These have extremal Sasaki metrics with constant scalar curvature. Moreover, we present further examples of both Sasaki-Einstein and Sasaki$\eta$Einstein metrics.