Geometry of Principal Sheaves
Seiten
2011
|
1st ed. Softcover of orig. ed. 2005
Springer (Verlag)
978-90-481-6858-3 (ISBN)
Springer (Verlag)
978-90-481-6858-3 (ISBN)
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.
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.
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.
| Reihe/Serie | Mathematics and Its Applications ; 578 |
|---|---|
| Zusatzinfo | XVI, 444 p. |
| Verlagsort | Dordrecht |
| Sprache | englisch |
| Maße | 160 x 240 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| ISBN-10 | 90-481-6858-9 / 9048168589 |
| ISBN-13 | 978-90-481-6858-3 / 9789048168583 |
| Zustand | Neuware |
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