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Results tagged with smooth-manifolds
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user 1004
Smooth manifolds and smooth functions between them. For manifolds with additional structure, see more specific tags, such as [riemannian-geometry]. For more topological aspects, see [differential-topology].
16
votes
On the $\mathbb R$-algebra structure on $C^\infty(M)$.
You can determine the R-algebra structure of $C^\infty(M)$ purely from its ring structure. As Robin Chapman mentions, the constant function 1M is uniquely determined by the fact that it is the identit …
- 17.1k
12
votes
Are submersions of differentiable manifolds flat morphisms?
I can show that this is true for your "simple" case.
If g(x,y) ∈ C∞(ℝ2) vanishes on x ≤ 0 then it decomposes as g(x,y) = a(x)G(x,y) where a(x) ∈ C∞(ℝ) vanishes on x ≤ 0 and G(x,y) ∈ C∞(ℝ2).
This …
- 17.1k
12
votes
Are submersions of differentiable manifolds flat morphisms?
I can get quite close to proving this. That doesn't mean that the result is true but it does at least seem to be very nearly true. We can also see what any counterexamples must look like if it does fa …
- 17.1k