Natural Operations in Differential Geometry

Ivan Kolar, Peter W. Michor, Jan Slovak (Autoren)

Buch | Softcover

VI, 434 Seiten

2010 | 1. Softcover reprint of hardcover 1st ed. 1993
Springer Berlin (Verlag)
978-3-642-08149-1 (ISBN)

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The aim of this work is threefold: First it should be a monographical work on natural bundles and natural op 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.

Natural operators and natural operations are an area of differential geometry that relates closely to problems in theoretical physics. So far there has been no book on the subject. This one therefore fills the gap and collects in an unified presentation the otherwise scattered material on the subject; it also includes a very comprehensive bibliography and will certainly be the standard reference for the next few years.

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.

Erscheint lt. Verlag	1.12.2010
Zusatzinfo	VI, 434 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	664 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Themenwelt	Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
Schlagworte	Category over Manifolds • Differential Geometry • Jet • manifold • Mathematical Physics • Natural Bundle • Natural Operator
ISBN-10	3-642-08149-5 / 3642081495
ISBN-13	978-3-642-08149-1 / 9783642081491
Zustand	Neuware