proposition 14.106 The curvature is horizontal, and measures non-integrability

open in the book · parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:4316 · p. 590

Rests on

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 ¶

Supports

depends_on proposition 14.114 Chern–Weil forms descend to the base ¶
- depends_on definition 14.115 Characteristic forms ¶

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`	→	Curvature $2$-form	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:4329
`depends_on`	→	A connection splits the tangent space	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:4329
`depends_on`	←	Chern–Weil forms descend to the base	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:5065
`proves`	←	ch:12-lie-groups-fibre-bundles@proof-43	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:4332