Topology and Geometry for Physics

  • Helmut Eschrig
Part of the Lecture Notes in Physics book series (LNP, volume 822)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Helmut Eschrig
    Pages 1-9
  3. Helmut Eschrig
    Pages 11-53
  4. Helmut Eschrig
    Pages 55-95
  5. Helmut Eschrig
    Pages 97-114
  6. Helmut Eschrig
    Pages 115-171
  7. Helmut Eschrig
    Pages 173-204
  8. Helmut Eschrig
    Pages 205-246
  9. Helmut Eschrig
    Pages 299-346
  10. Back Matter
    Pages 347-389

About this book

Introduction

A concise but self-contained introduction of the central concepts of modern topology and differential geometry on a mathematical level is given specifically with applications in physics in mind. All basic concepts are systematically provided including sketches of the proofs of most statements. Smooth finite-dimensional manifolds, tensor and exterior calculus operating on them, homotopy, (co)homology theory including Morse theory of critical points, as well as the theory of fiber bundles and Riemannian geometry, are treated. Examples from physics comprise topological charges, the topology of periodic boundary conditions for solids, gauge fields, geometric phases in quantum physics and gravitation.

Keywords

(Co)homology Exterior calculus Fiber bundles Geometric phases Riemannian geometry

Authors and affiliations

  • Helmut Eschrig
    • 1
  1. 1.IFW DresdenDresdenGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-14700-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 2011
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-642-14699-2
  • Online ISBN 978-3-642-14700-5
  • Series Print ISSN 0075-8450
  • Series Online ISSN 1616-6361