A diffeomorphism classification of 5- and 7-dimensional non-simply-connected homogeneous spaces

Abstract

In this thesis we classify non-simply-connected smooth closed 5- and 7-dimensional orientable manifolds with finite cyclic fundamental group up to diffeomorphism. <br /> The manifolds which we consider admit transitive actions of Lie groups and Einstein metrics of positive scalar curvature. One can describe these manifolds as total spaces of certain principal U(1)-fibre bundles over a product of complex projective spaces.