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

This two-volume monograph obtains fundamental notions and results of the standard differential geometry of smooth (CINFINITY) manifolds, without using differential calculus. Here, the sheaf-theoretic character is emphasised. This has theoretical advantages such as greater perspective, clarity and un...

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Bibliographic Details
Main Author: Mallios, Anastasios
Format: eBook
Language:English
Published: Dordrecht Springer Netherlands 1998, 1998
Edition:1st ed. 1998
Series:Mathematics and Its Applications
Subjects:
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
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505 0 |a 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 
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653 |a Harmonic analysis 
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520 |a This two-volume monograph obtains fundamental notions and results of the standard differential geometry of smooth (CINFINITY) 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