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Wir sind gerne für Sie daL’ inj´ ´ enuit´ ´ mˆ 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.
Produkteigenschaften
- Artikelnummer: 9789048168583
- Medium: Buch
- ISBN: 978-90-481-6858-3
- Verlag: Springer Netherlands
- Erscheinungstermin: 29.01.2011
- Sprache(n): Englisch
- Auflage: Softcover version of original hardcover Auflage 2005
- Serie: Mathematics and Its Applications
- Produktform: Kartoniert
- Gewicht: 729 g
- Seiten: 444
- Format (B x H x T): 160 x 240 x 25 mm
- Ausgabetyp: Kein, Unbekannt