Geometry of Principal Sheaves

Description

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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1. Ebooks list page : 1362
2. Geometry of Principal Sheaves
3. Lectures on Algebraic Geometry, 1: Sheaves, Cohomology of Sheaves, and Applications to Riemann Surfaces
4. Algebraic Geometry 2: Sheaves and Cohomology
5. The Geometry of Moduli Spaces of Sheaves
6. Sheaves in geometry and logic: A first introduction to topos theory
7. The Principal Portfolio
8. D-Modules, Perverse Sheaves, and Representation Theory
9. Sheaves in Topology (Universitext): Alexandru Dimca
10. Principal Leadership 01 2009
11. Principal Component Analysis
12. Compatibility, Stability, and Sheaves (Pure and Applied Mathematics)
13. Compatibility, Stability, and Sheaves (Pure and Applied Mathematics)
14. Surface Analysis: The Principal Techniques
15. A User's Guide to Principal Components
16. Principal Component Analysis (Repost)