Resumen de Deforming three-manifolds with positive scalar curvature

Fernando Codá Marques

• In this paper we prove that the moduli space of metrics with positive scalar curvature of an orientable compact three-manifold is path-connected. The proof uses the Ricci flow with surgery, the conformal method, and the connected sum construction of Gromov and Lawson. The work of Perelman on Hamilton�s Ricci flow is fundamental. As one of the applications we prove the path-connectedness of the space of trace-free asymptotically flat solutions to the vacuum Einstein constraint equations on R 3