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{\displaystyle X} , the it is a diffeomorphism. Thus, in general, I am not sure how a local diffeomorphism (that is not a diffeomorphism) might arise from a flow...

clarify that there are two notions of diffeomorphism, a diffeomorphism of smooth manifolds and a diffeomorphism of differentiable manifolds, and that...

ambient space. The Whitney umbrella point is an diffeomorphism invariant, i.e. you can take a local diffeomorphism (close to the origin) of the ambient space...

,X_n are n vector fields on a smooth n-manifold, then there's a local diffeomorphism F from a neighbourhood of a point p in M such that F(X_i) = d/(dx_i)...

implies that flows exist for all time for the $\tilde{X}_i$. Call the diffeomorphism obtained by flowing for time t along $\tilde{X}_i$ $\phi_i(t)$. Fix...

(UTC) OK, thanks. I guess another question then is, does the lack of a diffeomorphism mean that a sphere and an exotic sphere have different topologies, or...

sphere may be called Σn. Up to diffeomorphism, this structure depends only on the isotopy class of the diffeomorphism h. By contrast, a clutching map...

{\displaystyle \mathbb {S} ^{2}} , not equal. We need to provide the diffeomorphism associated with this invariance (making them conformally isomorphic)...

think it comes from the fact that an etale map is analogous to a local diffeomorphism, so if you draw a curve X etale over Y, this looks pretty much spread...

background independent. Same for diffeomorphism invariance, for example you can write maxwell's equations in a diffeomorphism invariant way that is perfectly...

either that there is no C^r-diffeomorphism L -> L' (strong sense) or that the identity map L -> L' is not a C^r-diffeomorphism (weak sense). I remember that...

definitions should be mentioned here. What I find worse is the word "diffeomorphism" in the same definition - it is not clear with respect to what structures...

article should really be called "diffeomorphism covariance". 3. The EFE is a tensor equation, hence automatically diffeomorphism covariant, but while this is...

imposing name diffeomorphism invariance. It concerns the coordinates physicists use to describe space and time. The principle of diffeomorphism invariance...

understand the diffeomorphism article? (This article is key). We can't talk about singularities of plane curves without talking about diffeomorphisms, they form...

incorporate your ideas. JocK 19:20, 15 November 2006 (UTC) Anosov diffeomorphism is a diffeomorphism i.e. a particular map un a manifold with some regolarity properties...

the mapping does no 'folding' at all. You can push forward via a local diffeomorphism, no problem. Charles Matthews 21:31, 9 Apr 2005 (UTC) Hmm, sorry...

studying cobordism. (Since classification of smooth manifolds up to diffeomorphism is impossible thanks to Markov and the presentation problem for fundamental...

teaches something about continuous maps versus local homeomorphisms (or smooth maps versus local diffeomorphisms). To prove that Euler angles cannot determine...

Riemannian geometry -- Curvature -- Cartan–Hadamard theorem -- Large diffeomorphism -- Bolza surface -- Vector bundle -- Vector field -- Pseudodifferential...