Global analysis, analysis on manifolds Concept
Diffeomorphism
Builds on Differentiable function of several variablesFunction of several variables
Summary
A diffeomorphism is a bijection between open sets, or between manifolds, such that both the map and its inverse are differentiable. Diffeomorphisms are the changes of coordinates of calculus, and they preserve all differentiable structure.
Reading path
To understand this page from the ground up, read these 6 pages in order. The foundations come first.
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- no evidence level
- Euclidean space object
- Function concept
- Total derivative concept
- Function of several variables concept
- Differentiable function of several variables concept
- Diffeomorphism concept
Where this leads
36 pages build on this one.
- h-cobordism theorem
- Takens's theorem
- Circle map
- Ehresmann's fibration theorem
- Sphere theorem
- Moser's trick
- Isometry of Riemannian manifolds
- Collar neighbourhood theorem
- Ebin's slice theorem
- Soul theorem
- Feedback linearization
- s-cobordism theorem
- Injectivity radius
- Finite determinacy theorem
- Normal coordinates
- Action-angle coordinates
- Tubular neighborhood theorem
- Morin singularities
- Stable map
- Zimmer's conjecture
- Open embedding theorem for Hilbert manifolds
- Shadowing lemma
- Fefferman's theorem on extension of biholomorphisms
- Smooth four-dimensional Poincaré conjecture
- Noether's second theorem
- Denjoy theorem on rotation number
- Symplectomorphism
- Whitney's theorem on folds and cusps
- Zimmer program
- Pesin theory
- Slice theorem
- Lie pseudogroup
- Sinai–Ruelle–Bowen measure
- Diffeomorphism group
- Noether's theorem
- Conformal geometry
Further reading
- Web https://en.wikipedia.org/wiki/Diffeomorphism, Definition
About this page
| Tag | 0KZZ70ZHXP |
|---|---|
| URI | m2://0KZZ70ZHXP |
| Aliases | smooth-isomorphism |
| Kind | concept |
| Writing | W1 stated |
| MSC | 58C25 |
| Specializes | Homeomorphism |
| Uses | Differentiable function of several variables, Function of several variables |
| Same as |
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What this page needs for W2
- edge instance_of in: at least two examples (0 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
The writing levels say how complete the text of a page is. They do not measure its truth.
What links here
Definitions
Used by
- h-cobordism theorem
- Takens's theorem
- Circle map
- Ehresmann's fibration theorem
- Sphere theorem
- Moser's trick
- Isometry of Riemannian manifolds
- Collar neighbourhood theorem
- Soul theorem
- Feedback linearization
- Injectivity radius
- Finite determinacy theorem
- Normal coordinates
- Action-angle coordinates
- Tubular neighborhood theorem
- Morin singularities
- Stable map
- Zimmer's conjecture
- Open embedding theorem for Hilbert manifolds
- Shadowing lemma
- Fefferman's theorem on extension of biholomorphisms
- Smooth four-dimensional Poincaré conjecture
- Denjoy theorem on rotation number
- Symplectomorphism
- Whitney's theorem on folds and cusps
- Zimmer program
- Pesin theory
- Lie pseudogroup
- Sinai–Ruelle–Bowen measure
- Diffeomorphism group
- Noether's theorem
- Conformal geometry