Geometry of Vector Sheaves
Subtitle: An Axiomatic Approach to Differential Geometry Volume II: Geometry. Examples and Applications
By: by Anastasios Mallios
Series: Mathematics and Its Applications -- 439; Mathematics and Its Applications -- 439
Publisher: Springer Netherlands
Published: 1998
Place of publication: Dordrecht
Language: eng
Format: [electronic resource] :
Number of pages: 882
ISBN-13: 9789401061025; 9789401150064
Subjects: Functional analysis; Harmonic analysis; Mathematics; Global differential geometry; Algebraic topology; Global analysis
Description: 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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