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  • Book
  • © 1998

Geometry of Vector Sheaves

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

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
    PDF

  2. Geometry

    1. Front Matter

      Pages xxiii-xxiii
      PDF

    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
      PDF

    2. Classical Theory

      • Anastasios Mallios
      Pages 277-298

  4. Back Matter

    Pages 387-438
    PDF
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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.
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Keywords

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Authors and Affiliations

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

    Anastasios Mallios

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Bibliographic Information

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Buy it now

eBook USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

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