Geometry of Vector Sheaves | An Axiomatic Approach to Differential Geometry Volume II: Geometry. Examples and Applications

Anastasios Mallios

ISBN 10: 0792350065 / ISBN 13: 9780792350064

Editore: Springer Netherland, 1998

Geometry of Vector Sheaves | An Axiomatic Approach to Differential Geometry Volume II: Geometry. Examples and Applications | Anastasios Mallios | Buch | 2 Bücher | Englisch | 1998 | Springer Netherland | EAN 9780792350064 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu Print on Demand. Codice articolo 102170420

Riassunto:

This two-volume monograph obtains fundamental notions and results of the standard differential geometry of smooth (C^INFINITY) manifolds, without using differential calculus. Here, the sheaf-theoretic character is emphasised. This has theoretical advantages such as greater perspective, clarity and unification, but also practical benefits ranging from elementary particle physics, via gauge theories and theoretical cosmology (`differential spaces'), to non-linear PDEs (generalised functions). Thus, more general applications, which are no longer `smooth' in the classical sense, can be coped with. The treatise might also be construed as a new systematic endeavour to confront the ever-increasing notion that the `world around us is far from being smooth enough'.
Audience: This work is intended for postgraduate students and researchers whose work involves differential geometry, global analysis, analysis on manifolds, algebraic topology, sheaf theory, cohomology, functional analysis or abstract harmonic analysis.

Contenuti: Part One: Vector Sheaves. General Theory. I. Sheaf Theory. II. II. Sheaves and Presheaves with Algebraic Structure. III. Sheaf Cohomology. IV. Linear and Multilinear Algebra of Vector Sheaves. V. Vector Sheaves and Cohomology. Appendix: Category Jargon. Bibliography. Notational Index. Subject Index. Part Two: Geometry. VI. Geometry of Vector Sheaves. A-Connections. VII. A-Connections. Local Theory. VIII. Curvature. IX. Characteristic Classes. Part Three: Examples and Applications. X. Classical Theory. XI. Sheaves and Presheaves with Topological Algebraic Structures. Bibliography. Notational Index. Subject Index.

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Titolo: Geometry of Vector Sheaves | An Axiomatic ...
Casa editrice: Springer Netherland
Data di pubblicazione: 1998
Legatura: Buch
Condizione: Neu