Anastasios Mallios

Geometry of Vector Sheaves (eBook, PDF)

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

• Format: PDF

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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Produktdetails

• Verlag: Springer Netherlands
• Seitenzahl: 438
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9789401150064
• Artikelnr.: 44064533

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.