Time: 9h00, Friday, October 9, 2015

Location: Room 4, Building A14, Institute of Mathematics, 18 Hoang Quoc Viet, Cau Giay, Hanoi

Abstract: The talk is concerning the effectiveness of Functional Analysis methods in Differential Geometry. Positiveness of scalar curvature and Ricci curvature requires vanishing the obstruction $\theta(M)$ which is computed in some KK-theory of C*-algebras index as a pairing of spin Dirac operator and Mishchenko-Fomenko bundle associated to the manifold. U. Pennig had proved that the obstruction $\theta(M)$ does not vanish if $M$ is an enlargeable closed oriented smooth manifold of even dimension larger than or equals to 3, the universal cover of which admits a spin structure. Using the equivariant cohomology of holonomy groupoids we prove the theorem in the general case without restriction of evenness of dimension.