Cohomological Aspects of Linear Connections

The following sections are included:

• An Introductory Example

  • Gauge Equivalence Between Linear Connections

• Cohomology of Flat Linear Connections

  • Cohomological Interpretation of Newton-Leibnitz Formula

  • Newton-Leibnitz formula for Linear Connections

• Maxwell's Equations

  • Minkowski Space

• Homotopy Formula for Linear Connections

  • Homotopic Fat Maps

  • ∇-homotopy

  • Integral of Time-dependent Forms

  • Homotopy Operator

  • Homotopy Formula

• Characteristic Classes

  • Linear Functions and Connections

  • Polynomials and Connections

  • Invariant Polynomials from Geometrical Point of View

  • Characteristic Polynomial of an Endomorphism

  • Multilinear Functions Corresponding to Determinants

  • Invariance of Det_r

  • Invariance of Det_r,l

  • Geometric Approach to Invariance

  • Dependence on ∇

  • Characteristic Classes

  • Naturalness of Characteristic Classes

  • β-Characteristic Classes

  • Special Characteristic Classes