Band 578
Geometry of Principal Sheaves
Aus der Reihe
Mathematics and Its Applications
-
- Hardcover
- Taschenbuch ausgewählt
-
Sprache:Englisch
Fr. 138.00
inkl. gesetzl. MwSt.,
Beschreibung
Produktdetails
Einband
Taschenbuch
Erscheinungsdatum
29.01.2011
Verlag
Springer NetherlandSeitenzahl
444
Maße (L/B/H)
24/16/2.5 cm
Gewicht
692 g
Auflage
Repr. 2005
Sprache
Englisch
ISBN
978-90-481-6858-3
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.
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