Topological Invariants of Principal G-Bundles with Singularities

principal G-bundle with singularities is a principal bundle π: P¯ → M with structure group G¯ which reduces to a subgroup G ⊂ G¯ on the set M \ Σ, where M is an n-dimensional compact manifold and Σ ⊂ M is a k-dimensional submanifold. For example, a vector field on an n-dimensional Riemannian manifol...