Geometry of Vector Sheaves

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

  • Anastasios┬áMallios

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

Table of contents

  1. Front Matter
    Pages i-xxi
  2. Geometry

    1. Front Matter
      Pages xxiii-xxiii
    2. Anastasios Mallios
      Pages 1-96
    3. Anastasios Mallios
      Pages 97-183
    4. Anastasios Mallios
      Pages 185-241
    5. Anastasios Mallios
      Pages 243-275
  3. Examples and Applications

    1. Front Matter
      Pages N1-N1
    2. Anastasios Mallios
      Pages 277-298
  4. Back Matter
    Pages 387-438

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.


Algebraic topology Characteristic class abstract harmonic analysis cohomology curvature differential geometry functional analysis harmonic analysis homology manifold

Authors and affiliations

  • Anastasios┬áMallios
    • 1
  1. 1.Department of MathematicsUniversity of AthensAthensGreece

Bibliographic information