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E-book
Author Vassiliou, E. (Efstathios)

Title Geometry of principal sheaves / by Efstathios Vassiliou
Published Dordrecht ; [Great Britain] : Springer, ©2005

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Description 1 online resource (xvi, 444 pages) : illustrations
Series Mathematics and its applications (Dordrecht) ; vol. 578
Mathematics and its applications (D. Reidel Publishing Company) ; vol. 578.
Contents Sheaves and all that -- The category of differential triads -- Lie sheaves of groups -- Principal sheaves -- Vector and associated sheaves -- Connections on principal sheaves -- Connections on vector and associated sheaves -- Curvature -- Chern-Weil theory -- Applications and further examples -- Bibliography -- List of symbols -- Subject index
Summary The book provides a detailed introduction to the theory of connections on principal sheaves in the framework of Abstract Differential Geometry (ADG). This is a new approach to differential geometry based on sheaf theoretic methods, without use of ordinary calculus. This point of view complies with the demand of contemporary physics to cope with non-smooth models of physical phenomena and spaces with singularities. Starting with a brief survey of the required sheaf theory and cohomology, the exposition then moves on to differential triads (the abstraction of smooth manifolds) and Lie sheaves of groups (the abstraction of Lie groups). Having laid the groundwork, the main part of the book is devoted to the theory of connections on principal sheaves, incorporating connections on vector and associated sheaves. Topics such as the moduli sheaf of connections, classification of principal sheaves, curvature, flat connections and flat sheaves, Chern-Weil theory, are also treated. The study brings to light fundamental notions and tools of the standard differential geometry which are susceptible of the present abstraction, and whose role remains unexploited in the classical context, because of the abundance of means therein. However, most of the latter are nonsensical in ADG
Bibliography Includes bibliographical references and index
Notes English
Print version record
In OhioLINK electronic book center
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Subject Geometry, Differential.
MATHEMATICS -- Geometry -- Differential.
Geometría diferencial
Geometry, Differential
Form Electronic book
ISBN 9781402034169
1402034164
1402034156
9781402034152
6610283885
9786610283880
1280283882
9781280283888