Resumen de Smooth structures and Einstein metrics on CP2#5,6,7CP2

Rares Rasdeaconu, Ioana Suvaina

• We show that each of the topological 4-manifolds , for k = 5, 6, 7, 8 admits a smooth structure which has an Einstein metric of scalar curvature s > 0, a smooth structure which carries an Einstein metric with s < 0 and infinitely many non-diffeomorphic smooth structures which do not admit Einstein metrics. We also exhibit new examples of higher dimensional manifolds carrying Einstein metrics of both positive and negative scalar curvature.