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Fat Manifolds and Linear Connections
Alexandre M. Vinogradov
(Author)
·
Alessandro de Paris
(Author)
·
World Scientific Publishing Company
· Hardcover
Fat Manifolds and Linear Connections - Vinogradov, Alexandre M. ; de Paris, Alessandro
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Synopsis "Fat Manifolds and Linear Connections"
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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All books in our catalog are Original.
The book is written in English.
The binding of this edition is Hardcover.
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