Manifolds And Local Structures: A General Theory

Local structures, like differentiable manifolds, fibre bundles, vector bundles and foliations, can be obtained by gluing together a family of suitable ‘elementary spaces’, by means of partial homeomorphisms that fix the gluing conditions and form a sort of ‘intrinsic atlas’, instead of the more usual system of charts living in an external framework.

An ‘intrinsic manifold’ is defined here as such an atlas, in a suitable category of elementary spaces: open Euclidean spaces, or trivial …