Geometry of Principal Sheaves

By Efstathios Vassiliou

Book Overview

L' inj enuit m eme d' un regard neuf (celui de la science l'est toujours) peut parfois clairer d' un jour nouveau d' anciens probl emes. J.Monod 77, p. 13] his book is intended as a comprehensive introduction to the theory of T principalsheaves andtheirconnections inthesettingofAbstractDi?- ential Geometry (ADG), the latter being initiated by A. Mallios'sGeometry of Vector Sheaves 62]. Based on sheaf-theoretic methods and sheaf - homology, the presentGeometry of Principal Sheaves embodies the classical theory of connections on principal and vector bundles, and connections on vector sheaves, thus paving the way towards a uni'ed (abstract) gauge t- ory and other potential applications to theoretical physics. We elaborate on the aforementioned brief description in the sequel. Abstract (ADG) vs. Classical Di'erential Geometry (CDG). M- ern di'erential geometry is built upon the fundamental notions of di'er- tial (smooth) manifolds and ?ber bundles, based, intheir turn, on ordinary di'erential calculus. However, the theory of smooth manifolds is inadequate to cope, for - stance, with spaces like orbifolds, spaces with corners, or other spaces with more complicated singularities. This is a rather unfortunate situation, since one cannot apply the powerful methods of di'erential geometry to them or to any spaces that do not admit an ordinary method of di'erentiation. The ix x Preface same inadequacy manifests in physics, where many geometrical models of physical phenomena are non-smooth.

• Format: Hardcover
• Language: English
• ISBN: 1402034156
• ISBN13: 9781402034152
• Release Date: May 2005
• Publisher: Springer
• Length: 444 Pages
• Weight: 1.81 lbs.
• Dimensions: 1.0" x 6.1" x 9.2"