Symmetry via Lie algebra cohomology

The Killing operator on a Riemannian manifold is a linear differential operator on vector fields whose kernel provides the infinitesimal Riemannian symmetries. The Killing operator is best understood in terms of its prolongation, which entails some simple tensor identities. These simple identities can be viewed as arising from the identification of certain Lie algebra cohomologies. The point is that this case provides a model for more complicated operators similarly concerned with symmetry.Comment: Conference proceedings: JARCS Sydney 2009 (The Australian-Japanese Workshop on Real and Complex Singularities held at the University of Sydney

Extensions of the coeffective complex

The coeffective differential complex on a symplectic manifold is extended both in length and in scope, unifying the constructions of various other authors.Comment: 9 page

Higher Order Connections

The purpose of this article is to present the theory of higher order connections on vector bundles from a viewpoint inspired by projective differential geometry

Conformally Fedosov manifolds

We introduce the notion of a conformally Fedosov structure and construct an associated Cartan connection. When an appropriate curvature vanishes, this allows us to construct a family of natural differential complexes akin to the BGG complexes from parabolic geometry.Comment: 28 pages. This is a substantial update to include BGG machinery and the construction of differential complexe