Torsion Free Connections, Topology, Geometry and Differential Operators on Smooth Manifolds
Torsions of connections on higher order cotangent bundles
By a torsion of a general connection on a fibered manifold we understand the Frölicher-Nijenhuis bracket of and some canonical tangent valued one-form (affinor) on . Using all natural affinors on higher order cotangent bundles, we determine all torsions of general connections on such bundles. We present the geometrical interpretation and study some properties of the torsions.
Torsions of connections on time-dependent Weil bundles
We introduce the concept of a dynamical connection on a time-dependent Weil bundle and we characterize the structure of dynamical connections. Then we describe all torsions of dynamical connections.
Total connections in Lie groupoids
A total connection of order in a Lie groupoid over is defined as a first order connections in the -st jet prolongations of . A connection in the groupoid together with a linear connection on its base, ie. in the groupoid , give rise to a total connection of order , which is called simple. It is shown that this simple connection is curvature-free iff the generating connections are. Also, an -th order total connection in defines a total reduction of the -th prolongation of to ....
Transformations of sheaf connections.
Tranverse foliations of Seifert bundles and self homeomorphism of the circle.
Travaux de S. S. Chern et J. Simons sur les classes caractéristiques