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Results tagged with smooth-manifolds
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user 27013
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].
5
votes
1
answer
335
views
Sufficient conditions for $\mathrm{Der}_k(A)$ to be f.g. projective
Let $k$ be a field and $A$ a commutative $k$-algebra. What are sufficient conditions for the module of derivations $\mathrm{Der}_k(A)$ to be finitely generated projective?
I'm looking for conditions w …
- 6,406
9
votes
Is the class of n-dimensional manifolds essentially small?
Already in dimension $0$, the collection of all manifolds in the sense of the OP is a proper class: any set, equipped with the discrete topology, is a $0$-dimensional manifold. In dimension $n$, one c …
- 6,406
12
votes
1
answer
408
views
Are algebras of smooth functions formally smooth?
Let $M$ be a manifold. Then is the ring of smooth functions $C^\infty(M,\mathbb{R})$ formally smooth over $\mathbb{R}$?
If it helps, feel free to assume that $M$ is compact.
(This is not a joke quest …
- 6,406
17
votes
Do rings of smooth functions differ from rings of continuous functions?
Another conceptually interesting way to see that the answer is negative is to make the following observations (related to Tom Goodwillie's answer):
For any topological space $X$, the algebra of real- …
- 6,406