Ebook: 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 (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.

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Content:
Front Matter....Pages i-xxi
Front Matter....Pages xxiii-xxiii
Geometry of Vector Sheaves. A-connections....Pages 1-96
A-connections. Local Theory....Pages 97-183
Curvature....Pages 185-241
Characteristic Classes....Pages 243-275
Front Matter....Pages N1-N1
Classical Theory....Pages 277-298
Sheaves and presheaves with topological algebraic structures....Pages 299-386
Back Matter....Pages 387-438

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Content:
Front Matter....Pages i-xxi
Front Matter....Pages xxiii-xxiii
Geometry of Vector Sheaves. A-connections....Pages 1-96
A-connections. Local Theory....Pages 97-183
Curvature....Pages 185-241
Characteristic Classes....Pages 243-275
Front Matter....Pages N1-N1
Classical Theory....Pages 277-298
Sheaves and presheaves with topological algebraic structures....Pages 299-386
Back Matter....Pages 387-438
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