definition A.302 Orientation

open in the book · appendices/A-long-proofs.tex:14993 · p. 2940

Rests on

depends_on definition 13.44 Atlas ¶
- depends_on definition 13.43 Coordinate system ¶
depends_on lemma A.301 Transformation of the top form ¶
- depends_on definition 13.102 Wedge product ¶
  - depends_on definition 13.98 $k$-form ¶
    - depends_on definition 13.83 Covector ¶
      - depends_on definition 13.81 Vector on a manifold ¶
    - depends_on definition 13.84 Tensor ¶
      - depends_on definition 13.83 Covector ¶ ↺
      - depends_on definition 13.81 Vector on a manifold ¶ ↺
  - depends_on equation 13.239 eq:mfd-dual-basis ¶
- depends_on equation 13.241 eq:mfd-antisimb ¶
- depends_on proposition 13.100 The space of $k$-forms ¶
  - depends_on definition 13.83 Covector ¶ ↺
  - depends_on definition 13.98 $k$-form ¶ ↺
  - depends_on definition 13.84 Tensor ¶ ↺
  - proves proof ch:11-manifolds-tensors-curvature@proof-20 ¶
- proves proof app:A-long-proofs@proof-189 ¶

Every logical edge within two steps of this node.

type	direction	node	provenance	where
`depends_on`	→	Atlas	declared	appendices/A-long-proofs.tex:15001
`depends_on`	→	Transformation of the top form	declared	appendices/A-long-proofs.tex:15001
`depends_on`	←	The induced orientation of the boundary	declared	appendices/A-long-proofs.tex:15223
`depends_on`	←	Integral over a chart	declared	appendices/A-long-proofs.tex:15032