Geometry of Principal Sheaves (Hardcover) (ISBN-13: 9781402034152)

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.

Author: Efstathios Vassiliou
ISBN-10: 1402034156
ISBN-13: 9781402034152
Publisher: Springer
Language: English
Published: 05/04/2005
Pages: 444
Format: Hardcover
Weight: 1.81lbs
Size: 9.21h x 6.14w x 1.00d