Geometry of Principal Sheaves (Hardcover, 2005 ed.)

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.

General

Imprint:	Springer-Verlag New York
Country of origin:	United States
Series:	Mathematics and Its Applications, 578
Release date:	May 2005
First published:	2005
Authors:	Efstathios Vassiliou
Dimensions:	232 x 156 x 25mm (L x W x T)
Format:	Hardcover
Pages:	444
Edition:	2005 ed.
ISBN-13:	978-1-4020-3415-2
Categories:	Books > Science & Mathematics > Mathematics > Geometry > Differential & Riemannian geometry Promotions
LSN:	1-4020-3415-6
Barcode:	9781402034152

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