Overview
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.
Full Product Details
Author: Efstathios Vassiliou
Publisher: Springer
Imprint: Springer
Edition: Softcover reprint of hardcover 1st ed. 2005
Volume: 578
Dimensions:
Width: 16.00cm
, Height: 2.30cm
, Length: 24.00cm
Weight: 0.729kg
ISBN: 9789048168583
ISBN 10: 9048168589
Pages: 444
Publication Date: 29 January 2011
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Paperback
Publisher's Status: Active
Availability: Out of stock
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Reviews
From the reviews of the first edition: The book provides an accessible, well-written monograph devoted to the theory of principal sheaves and their connections in the setting initiated by, Geometry of vector sheaves. ... It is designed also as a reference book with detailed expositions and complete and self-contained proofs. (Witold Mozgawa, Zentralblatt MATH, Vol. 1082, 2006)
From the reviews of the first edition: The book provides an accessible, well-written monograph devoted to the theory of principal sheaves and their connections in the setting initiated by, Geometry of vector sheaves. ... It is designed also as a reference book with detailed expositions and complete and self-contained proofs. (Witold Mozgawa, Zentralblatt MATH, Vol. 1082, 2006)
From the reviews of the first edition: The book provides an accessible, well-written monograph devoted to the theory of principal sheaves and their connections in the setting initiated by, Geometry of vector sheaves. ! It is designed also as a reference book with detailed expositions and complete and self-contained proofs. (Witold Mozgawa, Zentralblatt MATH, Vol. 1082, 2006)
From the reviews of the first edition: The book provides an accessible, well-written monograph devoted to the theory of principal sheaves and their connections in the setting initiated by, Geometry of vector sheaves. ... It is designed also as a reference book with detailed expositions and complete and self-contained proofs. (Witold Mozgawa, Zentralblatt MATH, Vol. 1082, 2006)
