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＜E-Book＞
Geometry of Vector Sheaves : An Axiomatic Approach to Differential Geometry Volume II: Geometry. Examples and Applications / by Anastasios Mallios
(Mathematics and Its Applications ; 439)

Edition	1st ed. 1998.
Publisher	(Dordrecht : Springer Netherlands : Imprint: Springer)
Year	1998
Language	English
Size	XXIII, 438 p : online resource
Authors	*Mallios, Anastasios author SpringerLink (Online service)
Subjects	LCSH:Geometry, Differential LCSH:Global analysis (Mathematics) LCSH:Manifolds (Mathematics) LCSH:Algebraic topology LCSH:Functional analysis LCSH:Harmonic analysis FREE:Differential Geometry FREE:Global Analysis and Analysis on Manifolds FREE:Algebraic Topology FREE:Functional Analysis FREE:Abstract Harmonic Analysis
Notes	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 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 HTTP:URL=https://doi.org/10.1007/978-94-011-5006-4

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