nLab infinity-Chern-Weil theory - contents

∞-Chern-Weil theory

∞-Chern-Simons theory

∞-Wess-Zumino-Witten theory

• Chern-Weil theory

• ∞-Chern-Weil theory introduction

Ingredients

• cohomology

  • differential cohomology

• ∞-Lie theory

  • Lie integration

• ∞-Lie algebra cohomology

  • Chevalley-Eilenberg algebra, Weil algebra, invariant polynomial

Connection

• ∞-Lie algebroid valued differential forms

• ∞-connection on a principal ∞-bundle

Curvature

• curvature

  • Bianchi identity

  • curvature characteristic form

  • covariant derivative

• secondary characteristic class

• Chern-Simons form

Theorems

• Chern-Weil homomorphism

• Chern-Gauss-Bonnet theorem

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