Sasakian Manifolds with Perfect Fundamental Groups
  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 greater than 1. These have extremal Sasaki metrics with constant scalar curvature. Moreover, we present further examples of both Sasaki-Einstein and Sasaki-$\eta$-Einstein metrics. 
Charles P. Boyer and Christina W. T{\o}nnesen-Friedman
math.DG math.SG