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Results tagged with smooth-manifolds
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user 22131
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].
19
votes
Accepted
Is each closed convex set a manifold with corners?
Consider the following curve (very informally described):
start from the origin in $\mathbb{R}^2$, then move from one unit up.
Turn of an angle $\pi/4$ on the left and move from half of unit.
Turn o …
- 42.4k
12
votes
Accepted
Does pullback in the category of smooth manifolds always exists?
If a pullback exists in the category of smooth manifold then, its underlying set of points has to be what you described simply by looking at morphism from the point. Moreover a map into the pullback i …
- 42.4k
11
votes
Accepted
Differential Topology over $\mathbb{Q}$
Claim : any rational manifold is a disjoint union of rational ball.
let's prove it for a countable rational manifold:
assume the point of $X$ are numbered $x_1,\dots,x_n...$.
Pick a neighbourhood …
- 42.4k
6
votes
Which category of sheaves on a manifold remembers the manifold?
Assuming the manifold is Hausdorff, the category of sheaves of modules over the sheaf of smooth functions do the trick.
This category is equivalent to the category of non-degenerate module over the r …
- 42.4k