Geometry of Principal Sheaves

Efstathios Vassiliou

ISBN 10: 9048168589 / ISBN 13: 9789048168583

Verlag: Springer Netherlands, Springer Netherlands Jan 2011, 2011

Beschreibung

Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 460 pp. Englisch.

Bestandsnummer des Verkäufers 9789048168583

Bibliografische Details

• Titel: Geometry of Principal Sheaves
• Verlag: Springer Netherlands, Springer Netherlands Jan 2011
• Erscheinungsjahr: 2011
• Sprache: Englisch
• ISBN-10: 9048168589
• ISBN-13: 9789048168583
• Einband: Taschenbuch
• Zustand: Neu

Über diesen Titel

Inhaltsangabe

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.

Críticas

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)