The tangent bundle as a disjoint union

Depends on

• Derivations at a point and the tangent space

Used by

• A smooth vector field is a smooth section of the tangent bundle Definition
• Cotangent space and cotangent bundle as a disjoint union Definition
• Formal immersion between smooth manifolds Definition
• Gauss frame map of an immersion into Euclidean space Definition
• Hermitian metric and L² pairing on a compact Riemann surface Definition
• Interior product of a form by a vector field Definition
• Nondegenerate zero of a vector field Definition
• Rotation number of an immersed oriented circle in the plane Definition
• Stable normal inverse of the tangent bundle Definition
• The frame bundle of a smooth manifold Definition
• The global differential or tangent map Definition
• The induced tangent bundle chart Definition
• The type (r,s) tensor bundle Definition
• Compact isotopic submanifolds have isomorphic normal bundles and diffeomorphic complements Example
• Self-intersection of the zero section in an oriented plane bundle Example
• The diagonal in the two-sphere has self-intersection two Example
• The standard sphere immersion and its normal line Example
• The velocity field of an isotopy is well defined along its image Lemma
• The index of a zero is its zero-section intersection number Proposition
• Assuming countable choice, the tangent bundle has a canonical smooth 2n-manifold structure Theorem

Dependency tree · two levels

3 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

• John M. Lee, Introduction to Smooth Manifolds (standard reference, not scraped)
• Will J. Merry, Differential Geometry (standard reference, not scraped)
• Nigel Hitchin, Differentiable Manifolds (standard reference, not scraped)