Efstathios Vassiliou Geometry of Principal Sheaves 9789048168583

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Автор: Efstathios Vassiliou
Название: Geometry of Principal Sheaves
ISBN: 9789048168583
Издательство: Springer
Классификация: ISBN-10: 9048168589
Обложка/Формат: Paperback
Страницы: 444
Вес: 0.64 кг.
Дата издания: 2005
Серия: Mathematics and Its Applications (closed)
Язык: English
Размер: 234 x 156 x 24
Читательская аудитория: Science
Ссылка на Издательство: Link
Поставляется из: Германии
Описание: L inj enuit m DEGREES eme d un regard neuf (celui de la science lest 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. MalliossGeometry 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.

Geometry of Principal Sheaves, Efstathios Vassiliou