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

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SUMMARY

This discussion centers on the two influential books by Naber, specifically "Topology, Geometry and Gauge Fields" and its companion volume. The texts cover essential mathematical concepts such as homotopy, homology, bundles, and characteristic classes while effectively linking these topics to physics. Participants express satisfaction with the rigor of the exercises, noting their effectiveness in deepening understanding. Recommendations for similar literature include works by Göckeler and Schücker, Raifertaigh, Nash, Atiyah, and others, highlighting the rich intersection of mathematics and physics.

PREREQUISITES
  • Understanding of homotopy and homology theories
  • Familiarity with fiber bundles and characteristic classes
  • Basic knowledge of differential geometry
  • Awareness of gauge theories in physics
NEXT STEPS
  • Explore Göckeler and Schücker's "Differential Geometry, Gauge Theories and Gravity"
  • Study Raifertaigh's "Group Structure of Gauge Theory"
  • Investigate Nash's "Differential Topology and Quantum Field Theory"
  • Read Atiyah's "Geometry of Yang-Mills Fields"
USEFUL FOR

This discussion is beneficial for mathematicians, physicists, and students interested in the interplay between topology, geometry, and gauge theories, particularly those seeking rigorous mathematical foundations in theoretical physics.

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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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.
 

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