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I am looking for introductory texts on Ehresmann connections and Chern-Simons forms. I seek detailed, hands-on presentation. Please, recommend sources that employ a differential forms approach rather then the algebro-topological one. Of course, the latter is also welcome.

Let me state my background. My understanding of homological group theory and algebraic topology is poor. I have basic knowledge of differential forms and differential topology. I am vaguely familiar with characteristic classes and invariant polynomials.

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  • $\begingroup$ Sounds like you are reading Nakahara's book? $\endgroup$
    – zzz
    Jun 16 '15 at 4:21
  • $\begingroup$ I am aware of Nakahara's book, and I will be reading it, @bechira. $\endgroup$ Jun 16 '15 at 9:49
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You're asking about two things:

  1. Ehresmann connections - the theory of connections over fibre bundles
  2. Chern-Simons form - a specific characteristic class

Given this, your question is essentially a duplicate of this other question.

For 1, see this thread and links therein.

For 2, I like:

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  • $\begingroup$ Thank you, Bechira. I am sorry but Morita treats not the construction of the Chern-Simons form. Moreover I find no mention of Chern-Simons theory in Bott & Tu. $\endgroup$ Jun 16 '15 at 10:25
  • $\begingroup$ It depends on whether you want to learn about chern Simons forms or chern Simons theory. The former is a characteristic class, once you get acquainted with characteristic classes there should be no issue with understanding it from review papers. The latter is a topological field theory due to Written, on which there are numerous physics textbooks, but this is not the correct site to ask for that. $\endgroup$
    – zzz
    Jun 16 '15 at 17:30
  • $\begingroup$ I beg your pardon. What are some physics textbooks treating Chern-Simons theory? $\endgroup$ Jun 16 '15 at 18:28
  • $\begingroup$ See this MO thread and this physics SE thread $\endgroup$
    – zzz
    Jun 16 '15 at 18:30
  • $\begingroup$ Thank you again. Which review papers do you recommend for Chern-Simons forms? $\endgroup$ Jun 17 '15 at 8:16

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