Cartan Geometries and Their Symmetries - Mike Crampin David Saunders Gebunden

In this book we first review the ideas of Lie groupoid and Lie algebroid and the associated concepts of connection. We next consider Lie groupoids of fibre morphisms of a fibre bundle and the connections on such groupoids together with their symmetries. We also see how the infinitesimal approach using Lie algebroids rather than Lie groupoids and in particular using Lie algebroids of vector fields along the projection of the fibre bundle may be of benefit.We then introduce Cartan geometries together with a number of tools we shall use to study them. We take as particular examples the fo ur classical types of geometry: affine projective Riemannian and conformal geometry. We also see how our approach can start to fit into a more general theory. Finally we specialize to the geometries (affine and projective) associated with path spaces and geodesics and consider their symmetries and other properties.