Geometry of Principal Sheaves by Efstathios VassiliouGeometry of Principal Sheaves by Efstathios Vassiliou

Geometry of Principal Sheaves

byEfstathios Vassiliou

Paperback | January 29, 2011

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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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Title:Geometry of Principal SheavesFormat:PaperbackDimensions:460 pages, 9.45 × 6.3 × 0.27 inPublished:January 29, 2011Publisher:Springer NetherlandsLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9048168589

ISBN - 13:9789048168583

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Table of 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.

Editorial 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)