Efstathios Vassiliou

Geometry of Principal Sheaves

• Broschiertes Buch

Produktbeschreibung

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.

Produktdetails

• Mathematics and Its Applications 578
• Verlag: Springer / Springer Netherlands
• Artikelnr. des Verlages: 978-90-481-6858-3
• Repr. 2005
• Seitenzahl: 460
• Erscheinungstermin: 29. Januar 2011
• Englisch
• Abmessung: 240mm x 160mm x 25mm
• Gewicht: 692g
• ISBN-13: 9789048168583
• ISBN-10: 9048168589
• Artikelnr.: 32094769

Inhaltsangabe

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.

Rezensionen

From the reviews of the first edition: "The book provides an accessible, well-written monograph devoted to the theory of principal sheaves and their connections in the setting initiated by, Geometry of vector sheaves. ... It is designed also as a reference book with detailed expositions and complete and self-contained proofs." (Witold Mozgawa, Zentralblatt MATH, Vol. 1082, 2006)