- Provides a relatively quick path to a special topic in differential geometry: principal bundles, whose properties are then described in some detail
- Presents important, modern geometric ideas in a form accessible to students and researchers in other areas
- No previous knowledge of differential geometry is assumed
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- About this Textbook
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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.
- About the authors
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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.
- Reviews
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“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)
- Table of contents (18 chapters)
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Introduction
Pages 1-5
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Basics of Manifolds
Pages 7-29
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Vector Bundles
Pages 31-48
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Vectors, Covectors, and All That
Pages 49-57
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Exterior Algebra and Differential Forms
Pages 59-79
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Table of contents (18 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Principal Bundles
- Book Subtitle
- The Classical Case
- Authors
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- Stephen Bruce Sontz
- Series Title
- Universitext
- Copyright
- 2015
- Publisher
- Springer International Publishing
- Copyright Holder
- Springer International Publishing Switzerland
- eBook ISBN
- 978-3-319-14765-9
- DOI
- 10.1007/978-3-319-14765-9
- Softcover ISBN
- 978-3-319-14764-2
- Series ISSN
- 0172-5939
- Edition Number
- 1
- Number of Pages
- XV, 280
- Number of Illustrations
- 85 b/w illustrations
- Topics
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