Geometry of principal sheaves / by Efstathios Vassiliou.
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 t...
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| Main Author: | |
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| Format: | Ebook |
| Language: | English |
| Published: |
Dordrecht ; [Great Britain] :
Springer,
[2005]
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| Series: | Mathematics and its applications (D. Reidel Publishing Company) ;
vol. 578. |
| Subjects: | |
| Online Access: | Springer eBooks |
| 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. |
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| Physical Description: | 1 online resource (xvi, 444 pages) : illustrations. |
| Format: | Mode of access: World Wide Web. |
| Bibliography: | Includes bibliographical references and index. |
| ISBN: | 1280283882 1402034164 9781280283888 9781402034169 |