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Results tagged with embeddings
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user 11142
1
vote
Polynomial (non-)embedding of a simplex in euclidean space
I am curious what you have tried, since writing the question as
$$\mathbf{f}(t) - \mathbf{f}(s) = \mathbf{w},$$
With $t, s$ constrained to lie in the simplex and $w$ constrained to have norm smaller …
- 96.4k
4
votes
Mathematical value of constructing sphere eversions
It depends on what you view as the purpose of mathematics is. If your view is constructivist (mine is), then proving that some object (in your case, a sphere eversion) exists is only the first (some w …
- 96.4k
0
votes
Contractibility of space of embeddings of a disc
I believe at least the second (and somewhat more tentatively, the first) of the questions is answered (in much greater generality) in:
Homotopy types of the components
of spaces of embeddings of compact …
- 96.4k
20
votes
Questions on J. F. Nash's answer about his errors in the proof of embedding theorem
"Excess dimensions": If a manifold can be topologically embedded in $\mathbb{R}^N,$ and you can prove that it can be isometrically embedded in $\mathbb{R}^M,$ then the quantity he is talking about is …
- 96.4k
2
votes
Number of non-equivalent graph embeddings
), except in genus $0.$
In genus $0,$ if the graph is $3$-connected, there are exactly two embeddings (which are equivalent if you allow orientation-reversing flips). … Kwak, Jin Ho; Lee, Jaeun, Enumeration of graph embeddings, Discrete Math. 135, No.1-3, 129-151 (1994). ZBL0813.05034. …
- 96.4k
10
votes
Accepted
embeddings of product of spheres in Euclidean spaces
This is asked on MSE, and answered (see Jim Belk's answer, which is NOT the accepted answer).
- 96.4k