Fat Manifolds And Linear Connections
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A01=Alessandro De Paris
A01=Alexandre M Vinogradov
Author_Alessandro De Paris
Author_Alexandre M Vinogradov
Category=PBKJ
Category=PBMW
Curvature
Differential Geometry
Differential Graded Algebras
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Fiber Bundle
Gauge Transformation
Linear Connection
Mathematical Physics
Parallel Transport
Theoretical Physics
Product details
- ISBN 9789812819048
- Publication Date: 29 Dec 2008
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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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.
