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Geometry of Vector Sheaves: An Axiomatic Approach to Differential Geometry Volume II: Geometry. Examples and Applications by Anastasios Mallios

Geometry of Vector Sheaves: An Axiomatic Approach to Differential Geometry Volume II: Geometry. Examples and Applications

by Anastasios Mallios
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Book cover type: Hardcover
  • ISBN13: 9780792350064
  • Binding: Hardcover
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Publication Date:
  • Pages: 438
  • Original Price: EUR 99.99
  • Language: English
  • Edition: 1998
  • Item Weight: 831 grams
  • BISAC Subject(s): Geometry / Differential, Mathematical Analysis, and Topology

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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