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Vassiliou

Geometry of Principal Sheaves

Medium: Buch
ISBN: 978-90-481-6858-3
Verlag: Springer Netherlands
Erscheinungstermin: 29.01.2011
Lieferfrist: bis zu 10 Tage

L’ 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
Autoren/Hrsg.

Autoren

Sheaves and all that.- The category of differential triads.- Lie sheaves of groups.- Principal sheaves.- Vector and associated sheaves.- Connections on principal sheaves.- Connections on vector and associated sheaves.- Curvature.- Chern-Weil theory.- Applications and further examples.