proposition 14.113 The Chern–Simons forms of degree $3$ and $5$

open in the book · parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:4983 · p. 597

Rests on

depends_on definition 14.112 Chern–Simons form ¶
- 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 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 ¶
depends_on definition 14.109 $G$-invariant polynomial ¶ ↺
depends_on equation 14.164 eq:lie-formcs1 ¶
proves proof ch:12-lie-groups-fibre-bundles@proof-47 ¶

Supports

depends_on proposition 14.117 The quadratic invariant and its Chern–Simons form ¶

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	Chern–Simons form	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:5006
`depends_on`	→	$G$-invariant polynomial	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:5006
`depends_on`	→	eq:lie-formcs1	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:5006
`depends_on`	←	The quadratic invariant and its Chern–Simons form	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:5194
`proves`	←	ch:12-lie-groups-fibre-bundles@proof-47	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:5009