Geometry of Vector Sheaves: An Axiomatic Approach to Differential Geometry Volume II: Geometry. Examples and Applications (Mathematics and Its Applications, 439)

Mallios, Anastasios

ISBN 10: 0792350065 / ISBN 13: 9780792350064

Published by Springer, 1998

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Bibliographic Details

• Title: Geometry of Vector Sheaves: An Axiomatic Approach to Differential Geometry Volume II: Geometry. Examples and Applications (Mathematics and Its Applications, 439)
• Publisher: Springer
• Publication Date: 1998
• Language: English
• ISBN 10: 0792350065
• ISBN 13: 9780792350064
• Binding: Hardcover
• Condition: Like New
• Book Type: book

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Synopsis

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.