© 2011

Topology, Geometry and Gauge fields



Part of the Texts in Applied Mathematics book series (TAM, volume 25)

Table of contents

  1. Front Matter
    Pages i-xx
  2. Gregory L. Naber
    Pages 1-25
  3. Gregory L. Naber
    Pages 27-96
  4. Gregory L. Naber
    Pages 97-156
  5. Gregory L. Naber
    Pages 157-213
  6. Gregory L. Naber
    Pages 215-232
  7. Gregory L. Naber
    Pages 233-329
  8. Gregory L. Naber
    Pages 331-392
  9. Gregory L. Naber
    Pages 393-401
  10. Gregory L. Naber
    Pages 403-420
  11. Back Matter
    Pages 421-437

About this book


This is a book on topology and geometry, and like any book on subjects as vast as these, it has a point of view that guided the selection of topics. The author’s point of view is that the rekindled interest that mathematics and physics have shown in each other of late should be fostered, and that this is best accomplished by allowing them to cohabit. The goal is to weave together rudimentary notions from the classical gauge theories of physics and the topological and geometrical concepts that became the mathematical models of these notions. The reader is assumed to have a minimal understanding of what an electromagnetic field is, a willingness to accept a few of the more elementary pronouncements of quantum mechanics, and a solid background in real analysis and linear algebra with some of the vocabulary of modern algebra. To such a reader we offer an excursion that begins with the definition of a topological space and finds its way eventually to the moduli space of anti-self-dual SU(2)-connections on S4 with instanton number -1. This second edition of the book includes a new chapter on singular homology theory and a new appendix outlining Donaldson’s beautiful application of gauge theory to the topology of compact, simply connected , smooth 4-manifolds with definite intersection form. Reviews of the first edition: “It is unusual to find a book so carefully tailored to the needs of this interdisciplinary area of mathematical physics…Naber combines a deep knowledge of his subject with an excellent informal writing style.” (NZMS Newsletter) "...this book should be very interesting for mathematicians and physicists (as well as other scientists) who are concerned with gauge theories." (ZENTRALBLATT FUER MATHEMATIK) “The book is well written and the examples do a great service to the reader. It will be a helpful companion to anyone teaching or studying gauge theory …” (Mathematical Reviews)


Connections Curvature Gauge Fields Homology Homotopy Instantons Lie Groups Magnetic Monopoles Manifolds Moduli Spaces Principal Bundles Topological spaces

Authors and affiliations

  1. 1.Department of Mathematics, Korman CenterDrexel UniversityPhiladelphiaUSA

About the authors

Gregory Naber is a Professor at Drexel University in the Department of Mathematics

Bibliographic information

  • Book Title Topology, Geometry and Gauge fields
  • Book Subtitle Foundations
  • Authors Gregory L. Naber
  • Series Title Texts in Applied Mathematics
  • Series Abbreviated Title Texts in Applied Math.
  • DOI
  • Copyright Information Springer Science+Business Media, LLC 2011
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-1-4419-7253-8
  • Softcover ISBN 978-1-4614-2682-0
  • eBook ISBN 978-1-4419-7254-5
  • Series ISSN 0939-2475
  • Edition Number 2
  • Number of Pages XX, 437
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Topology
    Elementary Particles, Quantum Field Theory
  • Buy this book on publisher's site


First Edition Review:

"Naber’s book, together with its predecessor[N4] subtitled Foundations, occupies a less populated niche in the market. This is the sector of teachable texts on differential geometry and its use in physics. Teachability does not refer to a definition-theorem-proof format. Nor does it imply anything about the depth of the treatment. Rather, it has to do with the organization of the topics, the selection of examples, the amount of instructive details provided, the ability to anticipate questions from the reader, and knowing when to stop."