Skip to main content
SpringerLink
Log in

Topology for Physicists

  • Book
  • © 1994

Overview

Authors:
  1. Albert S. Schwarz

    1. Department of Mathematics 565 Kerr Hall, University of California, Davis, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Grundlehren der mathematischen Wissenschaften (GL, volume 308)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 139.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 179.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 179.99
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

Licence this eBook for your library

Institutional subscriptions

Table of contents (16 chapters)

  1. Front Matter

    Pages I-XI
    Download chapter PDF

  2. Background

    • Albert S. Schwarz
    Pages 1-17

  3. Fundamental Concepts

    • Albert S. Schwarz
    Pages 19-32

  4. The Degree of a Map

    • Albert S. Schwarz
    Pages 33-43

  5. The Fundamental Group and Covering Spaces

    • Albert S. Schwarz
    Pages 45-57

  6. Manifolds

    • Albert S. Schwarz
    Pages 59-75

  7. Differential Forms and Homology in Euclidean Space

    • Albert S. Schwarz
    Pages 77-100

  8. Homology and Cohomology

    • Albert S. Schwarz
    Pages 101-157

  9. Homotopy Classification of Maps of the Sphere

    • Albert S. Schwarz
    Pages 159-166

  10. Homotopy Groups

    • Albert S. Schwarz
    Pages 167-172

  11. Fibered Spaces

    • Albert S. Schwarz
    Pages 173-183

  12. Fibrations and Homotopy Groups

    • Albert S. Schwarz
    Pages 185-189

  13. Homotopy Theory of Fibrations

    • Albert S. Schwarz
    Pages 191-207

  14. Lie Groups

    • Albert S. Schwarz
    Pages 209-216

  15. Lie Algebras

    • Albert S. Schwarz
    Pages 217-231

  16. Topology of Lie Groups and Homogeneous Manifolds

    • Albert S. Schwarz
    Pages 233-242

  17. Geometry of Gauge Fields

    • Albert S. Schwarz
    Pages 243-285

  18. Back Matter

    Pages 287-299
    Download chapter PDF
Back to top

Keywords

About this book

In recent years topology has firmly established itself as an important part of the physicist's mathematical arsenal. Topology has profound relevance to quantum field theory-for example, topological nontrivial solutions of the classical equa­ tions of motion (solitons and instantons) allow the physicist to leave the frame­ work of perturbation theory. The significance of topology has increased even further with the development of string theory, which uses very sharp topologi­ cal methods-both in the study of strings, and in the pursuit of the transition to four-dimensional field theories by means of spontaneous compactification. Im­ portant applications of topology also occur in other areas of physics: the study of defects in condensed media, of singularities in the excitation spectrum of crystals, of the quantum Hall effect, and so on. Nowadays, a working knowledge of the basic concepts of topology is essential to quantum field theorists; there is no doubt that tomorrow this will also be true for specialists in many other areas of theoretical physics. The amount of topological information used in the physics literature is very large. Most common is homotopy theory. But other subjects also play an important role: homology theory, fibration theory (and characteristic classes in particular), and also branches of mathematics that are not directly a part of topology, but which use topological methods in an essential way: for example, the theory of indices of elliptic operators and the theory of complex manifolds.

Authors and Affiliations

  • Department of Mathematics 565 Kerr Hall, University of California, Davis, USA

    Albert S. Schwarz

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation