Naber's Topology, geometry and gauge fields and similar books

In summary, the conversation discusses two books by Naber that cover mathematical topics such as homotopy, homology, bundles, and characteristic classes with connections to physics. The books are mathematically rigorous and the exercises are suitable for understanding the topics. Other recommended books on similar topics are göckeler and schücker's "Differential Geometry Gauge Theories and Gravity," raifertaigh's "Group Structure of Gauge Theory," nash's "Differential Topology and QFT," atiyah's "Geometry of Yang-Mills Fields," the Clay Mathematics Monograph "Mirror Symmetry," morita's "Geometry of Differential Forms," and michor's "Gauge Theory for Fiber Bundles."
  • #1
R136a1
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Hello,

This thread is about the two books by Naber:

https://www.amazon.com/dp/1461426820/?tag=pfamazon01-20
https://www.amazon.com/dp/0387989471/?tag=pfamazon01-20

The topics in this book seem excellent. They are standard mathematical topics such as homotopy, homology, bundles, characteristic classes, etc. But unlike math books, the links to physics are clearly displayed. Nevertheless, the book does remain mathematically rigorous.

If anybody here went through this text, what did you think about it? And did you find the exercises suitable enough to make you understand the topic (versus superficial exercises).

Does anybody know similar books to this one which are good?
 
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  • #2
hi. I read these books. I recommend reading: göckeler, schücker - differential geometry gauge theories and gravity, raifertaigh - group structure of Gauge theory, nash - differential topology and qft, atiyah - geometry of yang-mills fields, clay math.monograph - mirror symmetry, morita - geometry of diff. forms, peter michor - Gauge theory for fiber bundles (short lecture notes).

You can find further other books.
 

1. What is Naber's Topology, geometry and gauge fields book about?

Naber's Topology, geometry and gauge fields book is a comprehensive guide to the mathematical foundations of gauge theories in physics. It covers topics such as topology, geometry, and differential forms, and their applications in gauge field theories.

2. Who is the target audience for Naber's book?

The book is primarily intended for graduate and advanced undergraduate students in mathematics and physics, as well as researchers interested in the mathematical aspects of gauge theories.

3. How does Naber's book differ from other books on the same topic?

Naber's book stands out for its clear and rigorous treatment of the mathematical concepts underlying gauge theories. It also includes a wide range of examples and exercises to help readers understand the material.

4. Is prior knowledge of topology and geometry necessary to understand Naber's book?

Yes, a basic understanding of topology and geometry is necessary to fully grasp the concepts presented in Naber's book. However, the book does provide a brief review of these topics at the beginning.

5. Can Naber's book be used as a reference for researchers?

Yes, Naber's book can serve as a helpful reference for researchers in the field of mathematical physics. It covers a variety of topics in depth and provides a comprehensive overview of the mathematical foundations of gauge theories.

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