Anastasios Mallios

Geometry of Vector Sheaves

An Axiomatic Approach to Differential Geometry Volume II: Geometry. Examples and Applications

• Gebundenes Buch

Produktbeschreibung

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.

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Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.

Produktdetails

• Mathematics and Its Applications 439
• Verlag: Springer / Springer Netherlands
• Artikelnr. des Verlages: 978-0-7923-5006-4
• 1998.
• Seitenzahl: 936
• Erscheinungstermin: 30. April 1998
• Englisch
• Abmessung: 241mm x 160mm x 62mm
• Gewicht: 1771g
• ISBN-13: 9780792350064
• ISBN-10: 0792350065
• Artikelnr.: 21882161

Inhaltsangabe

Two. Geometry.- VI. Geometry of Vector Sheaves. A-connections.- VII. A-connections. Local Theory.- VIII. Curvature.- IX. Characteristic Classes.- Three. Examples and Applications.- X. Classical Theory.- XI. Sheaves and Presheaves with Topological Algebraic Structures.- Notational Index.