Geometry of Vector Sheaves: An Axiomatic Approach to Differential Geometry Volume II: Geometry. Examples and Applications
Author:   Anastasios Mallios
Publisher:   Springer
Edition:   Softcover reprint of the original 1st ed. 1998
Volume:   439
ISBN:  

9789401061025


Pages:   438
Publication Date:   08 October 2012
Format:   Paperback
Availability:   Manufactured on demand   Availability explained
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Geometry of Vector Sheaves: An Axiomatic Approach to Differential Geometry Volume II: Geometry. Examples and Applications


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Overview

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.

Full Product Details

Author:   Anastasios Mallios
Publisher:   Springer
Imprint:   Springer
Edition:   Softcover reprint of the original 1st ed. 1998
Volume:   439
Dimensions:   Width: 16.00cm , Height: 2.40cm , Length: 24.00cm
Weight:   0.742kg
ISBN:  

9789401061025


ISBN 10:   9401061025
Pages:   438
Publication Date:   08 October 2012
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand   Availability explained
We will order this item for you from a manufactured on demand supplier.

Table of Contents

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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