Introductions to Ehresmann connections and Chern-Simons forms

Question

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.

Answer 1

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:

• Morita
• Later chapters of Bott & Tu