Timeline for Bounding the dimension of the euclidean space in which any $n$-manifold embeds "$k$-uniquely" in it

5 events

when toggle format	what		by	license	comment
May 29, 2018 at 1:24	comment	added	Ben Wieland		Yes, $2n+k+1$. General position gives $2n+k+2$ and the Whitney trick peels off another dimension. The key is to rewrite $\pi_iEmb(M,\mathbb R^n)$ as a map $M\times S^i\to \mathbb R^n\times S^i$. This is much better than $M\times S^i\to\mathbb R^n$. It is redundant (and you have to make sure that such redundancy is preserved as you manipulate it), but the self-intersections of such maps are the obstruction to parameterized embedding. Extend to a map $M\times D^{i+1}\to \mathbb R^n\times D^{i+1}$. Apply general position to this new map.
May 22, 2018 at 13:41	history	edited	Saal Hardali	CC BY-SA 4.0	edited title; added 1 character in body; deleted 31 characters in body
May 22, 2018 at 12:08	history	edited	Saal Hardali	CC BY-SA 4.0	deleted 2 characters in body
May 22, 2018 at 11:49	history	edited	Saal Hardali	CC BY-SA 4.0	deleted 12 characters in body
May 22, 2018 at 11:42	history	asked	Saal Hardali	CC BY-SA 4.0