Generalised Connections and Curvature

Abstract

The concept of generalised (in the sense of Colombeau) connection on a principal fibre bundle is introduced. This definition is then used to extend results concerning the geometry of principal fibre bundles to those that only have a generalised connection. Some applications to singular solutions of Yang-Mills theory are given.

29 pages, added a result on generalized de Rham cohomology (Prop. 8.2)

References in corpus (3)

• On the foundations of nonlinear generalized functions I
• Foundations of a nonlinear distributional geometry
• On Singular Connections and Geometrically Atomic Maps

Cited by in corpus (10)

• The use of Generalised Functions and Distributions in General Relativity
• On the Geroch-Traschen class of metrics
• Microlocal analysis in the dual of a Colombeau algebra: generalized wave front sets and noncharacteristic regularity
• Colombeau algebra as a mathematical tool for investigating step load and step deformation of systems of nonlinear springs and dashpots
• The sequence of ideas in a re-discovery of the Colombeau algebras
• The wave equation on static singular space-times
• Suppleness of the sheaf of algebras of generalized functions on manifolds
• Foundations of the calculus of variations in generalized function algebras
• Geometrical embeddings for distributions into algebras of generalized functions
• Wave equations on space-times of low regularity: Existence results and regularity theory in the framework of generalized function algebras