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I am looking for a good reference for fibre bundles on differential manifolds, Ehresmann connections, principal $G$-bundles and principal Ehresmann connections (the $G$-equivariant version of Ehresmann connections). Could anyone advise me on this? I have looked at the book Fibre Bundles by Hausmöller, but it isn't quite what I want.

Thanks in advance.

Armando j18eos
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Daniel Robert-Nicoud
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2 Answers2

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I can suggest:

  • Kobayashi S., Nomizu K. - Foundations of Differential Geometry; Volume 1, Chapter 2 and Note 1; Volume 2, Chapter 9, Subsection 3 and Note 12.
  • Kolář I., Michor P. W., Slovák J. - Natural Operations in Differential Geometry, Chapters 3 and 4;
  • Spivak M. - A comprehensive introduction to differential geometry, Volume II, Chapter 8;

where only the third book is easy and intuitive.

Armando j18eos
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2

Late to the party, but: Chapter 6 in Loring Tu's Differential Geometry: Connections, Curvature, and Characteristic Classes seems friendly enough, and well explained. I think sections §27 and §28 are what you're looking for.

Ivo Terek
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