definition 14.115 Characteristic forms

Rests on

• depends_on definition 14.109 $G$-invariant polynomial ¶
  • depends_on equation 14.144 eq:lie-invpol-linear ¶
  • depends_on equation 14.145 eq:lie-invpol-symm ¶
• depends_on proposition 14.114 Chern–Weil forms descend to the base ¶
  • depends_on definition 14.109 $G$-invariant polynomial ¶ ↺
  • depends_on proposition 14.106 The curvature is horizontal, and measures non-integrability ¶
    • depends_on definition 14.105 Curvature $2$-form ¶
      • depends_on definition 14.103 Connection $1$-form ¶
        • depends_on definition 14.97 Principal bundle ¶
        • depends_on notation 14.101 Algebra-valued forms and their bracket ¶
      • depends_on notation 14.101 Algebra-valued forms and their bracket ¶ ↺
    • depends_on proposition 14.104 A connection splits the tangent space ¶
      • depends_on definition 14.103 Connection $1$-form ¶ ↺
      • proves proof ch:12-lie-groups-fibre-bundles@proof-42 ¶
    • proves proof ch:12-lie-groups-fibre-bundles@proof-43 ¶
  • depends_on theorem 14.111 Chern–Weil ¶
    • depends_on equation 14.142 eq:lie-bianchi ¶
    • depends_on equation 14.139 eq:lie-curvature ¶
    • depends_on theorem 14.110 thm:lie-invpoly ¶
      • depends_on definition 14.109 $G$-invariant polynomial ¶ ↺
      • depends_on equation 14.5 eq:lie-structconst ¶
        • step_from equation 14.4 eq:lie-gengrlie ¶
      • proves proof ch:12-lie-groups-fibre-bundles@proof-45 ¶
    • proves proof ch:12-lie-groups-fibre-bundles@proof-46 ¶
  • proves proof ch:12-lie-groups-fibre-bundles@proof-48 ¶
• depends_on theorem 14.111 Chern–Weil ¶ ↺

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