MANIFOLDS AND LOCAL STRUCTURES
Marco Grandis
Gebundenes Buch

MANIFOLDS AND LOCAL STRUCTURES

A GENERAL THEORY

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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 bundles, or trivial vector bundles, and so on. This uniform approach allows us to move from one basis to anothe...