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Geometry of Vector Sheaves

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

  • Book
  • © 1998

Overview

Authors:
  1. Anastasios Mallios

    1. Department of Mathematics, University of Athens, Athens, Greece

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Part of the book series: Mathematics and Its Applications (MAIA, volume 439)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xxi
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  2. Geometry

    1. Front Matter

      Pages xxiii-xxiii
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    2. Geometry of Vector Sheaves. A-connections

      • Anastasios Mallios
      Pages 1-96

    3. A-connections. Local Theory

      • Anastasios Mallios
      Pages 97-183

    4. Curvature

      • Anastasios Mallios
      Pages 185-241

    5. Characteristic Classes

      • Anastasios Mallios
      Pages 243-275

  3. Examples and Applications

    1. Front Matter

      Pages N1-N1
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    2. Classical Theory

      • Anastasios Mallios
      Pages 277-298

    3. Sheaves and presheaves with topological algebraic structures

      • Anastasios Mallios
      Pages 299-386

  4. Back Matter

    Pages 387-438
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics, University of Athens, Athens, Greece

    Anastasios Mallios

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