Author	Kolรกล, Ivan. author
Title	Natural Operations in Differential Geometry [electronic resource] / by Ivan Kolรกล, Jan Slovรกk, Peter W. Michor
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1993
Connect to	http://dx.doi.org/10.1007/978-3-662-02950-3
Descript	VI, 434 p. online resource

The aim of this work is threefold: First it should be a monographical work on natural bundles and natural opยญ erators in differential geometry. This is a field which every differential geometer has met several times, but which is not treated in detail in one place. Let us explain a little, what we mean by naturality. Exterior derivative commutes with the pullback of differential forms. In the background of this statement are the following general concepts. The vector bundle A kT* M is in fact the value of a functor, which associates a bundle over M to each manifold M and a vector bundle homomorphism over f to each local diffeomorphism f between manifolds of the same dimension. This is a simple example of the concept of a natural bundle. The fact that exterior derivative d transforms sections of A kT* M into sections of A k+1T* M for every manifold M can be expressed by saying that d is an operator from A kT* M into A k+1T* M

I. Manifolds and Lie Groups -- II. Differential Forms -- III. Bundles and Connections -- IV. Jets and Natural Bundles -- V. Finite Order Theorems -- VI. Methods for Finding Natural Operators -- VII. Further Applications -- VIII. Product Preserving Functors -- IX. Bundle Functors on Manifolds -- X. Prolongation of Vector Fields and Connections -- XI. General Theory of Lie Derivatives -- XII. Gauge Natural Bundles and Operators -- References -- List of symbols -- Author index

1. Mathematics
2. Geometry
3. Differential geometry
4. Quantum physics
5. Quantum computers
6. Spintronics
7. Mathematics
8. Differential Geometry
9. Quantum Information Technology
10. Spintronics
11. Geometry
12. Quantum Physics