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" Geometry of Vector Sheaves "
by Anastasios Mallios.
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BL
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579658
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b408877
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| Main Entry
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Mallios, Anastasios.
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| Title & Author
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Geometry of Vector Sheaves : An Axiomatic Approach to Differential Geometry Volume II: Geometry. Examples and Applications /\ by Anastasios Mallios.
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| Publication Statement
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Dordrecht :: Springer Netherlands :: Imprint: Springer,, 1998.
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| Series Statement
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Mathematics and Its Applications ;; 439
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| ISBN
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9789401150064
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: 9789401061025
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| Contents
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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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| Abstract
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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.
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Mathematics.
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Harmonic analysis.
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Functional analysis.
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Global analysis.
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Global differential geometry.
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Algebraic topology.
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SpringerLink (Online service)
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