All Questions
5 questions
36
votes
2
answers
5k
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Kervaire invariant: Why dimension 126 especially difficult?
Is there any resource that might help non-experts gains some understanding of why
the Kervaire invariant problem remains open now only in dimension $126$? ($126 =2^7-2=2^{j+1}-2$;
whether $\theta_j=\...
- 151k
34
votes
1
answer
4k
views
Strong Whitney embedding theorem for non-compact manifolds
$\newcommand{\RR}{\mathbb{R}}$The present question arises from some confusion on my part regarding the precise statement of the strong Whitney embedding theorem for non-compact manifolds.
The strong ...
- 6,210
29
votes
2
answers
2k
views
Contractibility of the space of Jordan curves
Is the space of Jordan curves in $\textbf{R}^2$ contractible? In other words, is there a canonical or continuous way to deform each Jordan curve to the unit circle $\textbf{S}^1$.
If the curves are ...
- 7,149
15
votes
2
answers
1k
views
Is there a citeable reference for star-shaped open subsets of R^n being diffeomorphic to R^n?
A folk theorem says that star-shaped open subsets of R^n are diffeomorphic to R^n.
Is there a citeable reference for a proof of this result?
For the sake of being definite, let's say that
“citeable” ...
- 37.8k
4
votes
1
answer
733
views
Reference request: Intrinsic definition of the strong Whitney topology on $\mathcal{C}^{\infty}(M,\mathbb{R})$ without using charts or jets
Let $M$ and $N$ be smooth manifolds. There is a description of the strong Whitney topology on $\mathcal{C}^{\infty}(M,N)$ in terms of partial derivative in charts (using locally finite sets of charts ...
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