Questions tagged [embeddings]
The embeddings tag has no usage guidance.
14 questions
4
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Generalizations of Abhyankar-Moh theorem (embeddings of the line in the plane)
Abhyankar-Moh theorem says that if $L$ is a complex line in the complex affine plane $\mathbb{C}^2$, then every embedding of $L$ into $\mathbb{C}^2$ extends to an automorphism of the plane.
It seems ...
- 2,837
26
votes
2
answers
4k
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Questions on J. F. Nash's answer about his errors in the proof of embedding theorem
In the interview of John Nash taken by Christian Skau and Martin Gaussen, in EMS Newsletter, September, 2015 when asked
Is it true, as rumours have it, that
you started to work on the embedding ...
- 541
16
votes
3
answers
2k
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When does a CW-complex of dimension 2 embed in $\Bbb R^4$?
Let $X$ be a finite CW-complex of dimension two having just one 0-cell
(+ finitely many 1-cells + finitely many 2-cells).
Is it true that X can be embedded in $\Bbb R^4$?
If true, is it due to ...
14
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0
answers
416
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Monotone embedding of complete binary tree in hypercube
Embedding different graphs, especially binary trees, in the hypercube has a huge literature. However, I could not find anything if we restrict the embedding to be monotone. So I would like to ...
- 18.9k
13
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3
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2k
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When does homology represent an embedded sphere?
If we have a triangulation of a manifold $M$ of dimension $i$ and we have simplicial homology $H_i(M)=\mathbb{Z}$, what is the condition than there exists an embedded sphere $S^i$ that generates the ...
- 1,465
10
votes
1
answer
796
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Is there a Nash-type theorem for symplectic manifolds?
If $(M, \omega)$ is a symplectic manifold, is it possible to embed (or injectively immerse) it symplectically into a sufficiently large $(\Bbb R ^{2N}, \Omega)$, (with the usual symplectic structure)?
...
- 5,407
8
votes
1
answer
264
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Does the continuous image of a disc contain an embedded disc?
Let $\phi:\Bbb D^2\to\Bbb R^n$ be a continuous mapping of the 2-disc $\Bbb D^2$ that is injective on the boundary $\partial\Bbb D^2=\Bbb S^1$. Does its image contain an embedded disc with the same ...
- 13.6k
7
votes
2
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3k
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Embeddings of flag manifolds
Consider the flag manifold $\mathbb{F}(a_1,\dots,a_k)$ parametrizing flags of type $F^{a_1}\subseteq\dots\subseteq F^{a_k}\subseteq V$ in a vector spaces $V$ of dimension $n+1$, where $F^{a_i}$ is a ...
user61586
6
votes
1
answer
375
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Different flavours of Vassiliev Conjecture
There is something that puzzles me about "Vassiliev's Conjecture". I am sure I am missing some detail which is obvious to the community, since there are several tightly related kind of ...
- 2,152
4
votes
1
answer
169
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"Almost embedding" the complete 2-dimensional complex $\mathcal K_7^2$ into $\Bbb R^4$
Let $\mathcal K_7^2$ be the complete 2-dimensional simplicial complex on seven vertices, i.e. it has all $7\choose 2$ edges and all $7\choose 3$ 2-simplices (and no higher-dimensional simplices).
I ...
- 13.6k
4
votes
1
answer
456
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Which topological spaces admit embeddings into Euclidean spaces
I'm interested in the dual question to:
continuous images of open intervals, about surjections onto open intervals.
Namely, if $X$ is a topological space, when can we guarantee that there exists a ...
- 5,405
4
votes
0
answers
181
views
Specify the embedding of special unitary group in a Spin group via their representation map
How do we specify the embedding of a Lie group $G_1$ as a subgroup into a larger Lie group $G_2$, with $G_1 \subset G_2$ that agree with a constraint on the mapping between their representations?
By ...
- 10.5k
4
votes
1
answer
700
views
Embedding graphs into hyperbolic spaces
Do we know of a characterization as to when does a graph have a "good" embedding into a hyperbolic space? (And does having such an embedding have a spectral or wavelet analysis signature?)
I don't ...
- 617
3
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115
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Isometric embeddings of $c_0$ into metric spaces
Are there any nice and useful criteria or theorems which assert when a given metric space $M$ contains an isometric (not necessarily linear) copy of the Banach space $c_0$ or its unit ball $B_{c_0}$? (...
- 1,151