Fat manifolds and linear connections / Alessandro De Paris, Alexandre Vinogradov.Material type: TextPublication details: Hackensack, NJ : World Scientific, ©2009. Description: 1 online resource (xii, 297 pages) : illustrationsContent type: text Media type: computer Carrier type: online resourceISBN: 9789812819055; 9812819053Subject(s): Differential calculus | Commutative algebra | Manifolds (Mathematics) | Algebras, Linear | MATHEMATICS -- Differential Equations -- General | Algebras, Linear | Commutative algebra | Differential calculus | Manifolds (Mathematics)Genre/Form: Electronic books. | Electronic books. Additional physical formats: Print version:: Fat manifolds and linear connections.DDC classification: 515/.33 LOC classification: QA304 | .D47 2009ebOnline resources: Click here to access online
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Includes bibliographical references (pages 281-282) and index.
Elements of differential calculus over commutative algebras -- Basic differential calculus on fat manifolds -- Linear connections -- Covariant differential -- Cohomological aspects of linear connections.
Print version record.
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.