Geometry of Principal Sheaves (Paperback, Softcover reprint of hardcover 1st ed. 2005)

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
Country of origin:	Netherlands
Series:	Mathematics and Its Applications, 578
Release date:	2011
First published:	2005
Authors:	Efstathios Vassiliou
Dimensions:	240 x 160 x 23mm (L x W x T)
Format:	Paperback
Pages:	444
Edition:	Softcover reprint of hardcover 1st ed. 2005
ISBN-13:	978-90-481-6858-3
Categories:	Books > Science & Mathematics > Mathematics > Geometry > Differential & Riemannian geometry
LSN:	90-481-6858-9
Barcode:	9789048168583

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