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The Cartan relations
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Classroom Contents
Singular Chains on Lie Groups and the Cartan Relations
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- 1 Intro
- 2 Outline
- 3 Lie theory
- 4 The group ring and singular chains
- 5 The Cartan relations
- 6 An equivalence of categories
- 7 How the proof works
- 8 Chern-Weil theory
- 9 Chern-Weil homomorphism
- 10 A dg-category of representations of Tg
- 11 A dg-category of modules over C(G)
- 12 Ingredients of the proof
- 13 Chen's iterated integrals
- 14 Bott-Shulman-Stasheff algebra
- 15 Ax de Rham theorem for classifying spaces
- 16 The non-commutative Weil algebra
- 17 The Moore Loop space
- 18 Example 1: The trivial representation
- 19 Example II: Free loop space of BG
