proposition 14.114 Chern–Weil forms descend to the base

open in the book · parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:5055 · p. 598

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 14.106 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 definition 14.95 Fibre 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 ¶
      - step_from equation 14.3 eq:lie-generators ¶
      - step_from equation 14.2 eq:lie-varincor ¶
  - 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 ¶

Every logical edge within two steps of this node.

type	direction	node	provenance	where
`depends_on`	→	$G$-invariant polynomial	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:5065
`depends_on`	→	The curvature is horizontal, and measures non-integrability	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:5065
`depends_on`	→	Chern–Weil	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:5065
`depends_on`	←	Characteristic forms	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:5125
`proves`	←	ch:12-lie-groups-fibre-bundles@proof-48	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:5068