Fat Manifolds and Linear Connections

Name: Fat Manifolds and Linear Connections
Brand: World Scientific Publishing Company
SKU: 9789812819048
Price: 12613.0 INR
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by Alexandre M. Vinogradov , Alessandro de Paris

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ISBN13: 9789812819048
Binding: Hardcover
Subject: N/A
Publisher: World Scientific Publishing Company
Publisher Imprint: World Scientific Publishing Company
Publication Date: December 1, 2008
Pages: 312
Original Price: USD 117.0
Language: English
Edition: N/A
Item Weight: 577 grams
BISAC Subject(s): Geometry / Differential

About The Book

The theory of connections is central not only in pure mathematics (differential and algebraic geometry), but also in mathematical and theoretical physics (general relativity, gauge fields, mechanics of continuum media). The now-standard approach to this subject was proposed by Ch. Ehresmann 60 years ago, attracting first mathematicians and later physicists by its transparent geometrical simplicity. Unfortunately, it does not extend well to a number of recently emerged situations of significant importance (singularities, supermanifolds, infinite jets and secondary calculus, etc.). Moreover, it does not help in understanding the structure of calculus naturally related with a connection.In this unique book, written in a reasonably self-contained manner, the theory of linear connections is systematically presented as a natural part of differential calculus over commutative algebras. This not only makes easy and natural numerous generalizations of the classical theory and reveals various new aspects of it, but also shows in a clear and transparent manner the intrinsic structure of the associated differential calculus. The notion of a "fat manifold" introduced here then allows the reader to build a well-working analogy of this "connection calculus" with the usual one.

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