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© 2015

Principal Bundles

The Classical Case

Textbook

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Stephen Bruce Sontz
    Pages 1-5
  3. Stephen Bruce Sontz
    Pages 7-29
  4. Stephen Bruce Sontz
    Pages 31-48
  5. Stephen Bruce Sontz
    Pages 49-57
  6. Stephen Bruce Sontz
    Pages 59-79
  7. Stephen Bruce Sontz
    Pages 81-91
  8. Stephen Bruce Sontz
    Pages 93-103
  9. Stephen Bruce Sontz
    Pages 105-110
  10. Stephen Bruce Sontz
    Pages 111-119
  11. Stephen Bruce Sontz
    Pages 121-144
  12. Stephen Bruce Sontz
    Pages 145-150
  13. Stephen Bruce Sontz
    Pages 151-172
  14. Stephen Bruce Sontz
    Pages 173-193
  15. Stephen Bruce Sontz
    Pages 195-223
  16. Stephen Bruce Sontz
    Pages 225-232
  17. Stephen Bruce Sontz
    Pages 233-246
  18. Stephen Bruce Sontz
    Pages 247-247
  19. Stephen Bruce Sontz
    Pages C1-C2
  20. Back Matter
    Pages 249-280

About this book

Introduction

This introductory graduate level text provides a relatively quick path to a special topic in classical differential geometry: principal bundles.  While the topic of principal bundles in differential geometry has become classic, even standard, material in the modern graduate mathematics curriculum, the unique approach taken in this text presents the material in a way that is intuitive for both students of mathematics and of physics. The goal of this book is to present important, modern geometric ideas in a form readily accessible to students and researchers in both the physics and mathematics communities, providing each with an understanding and appreciation of the language and ideas of the other.

Keywords

Connections Curvature Differential geometry Non-commutative geometry Principal bundles

Authors and affiliations

  1. 1.Centro de Investigación en Matemáticas, A.C.GuanajuatoMexico

About the authors

Stephen Bruce Sontz is a Professor at Centro de Investigacion en Matematicas (CIMAT).  He received his Ph.D. from the University of Virginia, USA, in 1994.

Bibliographic information

Industry Sectors
Aerospace

Reviews

“He has written a book about principal bundles in the classical sense which is of great interest in and of itself … . a textbook which can be used in an advanced one-year course or for self-learning. … the book is also interesting for a physicist, because one can find the geometric basis of many mathematical tools used in physics. … reviewer has greatly enjoyed reading the book and acknowledges the author’s bravery in writing another text on differential geometry!” (Fernando Etayo Gordejuela, Mathematical Reviews, November, 2015)

“The present book deals with principle bundles and their relevance in physics with a ground work on differential geometry. … The book will be helpful to the graduate and under graduate students of mathematics and physics. It can also be an informative hand book of the researchers in differential geometry and physics.” (Uday Chand De, zbMATH 1321.53004, 2015)