Timeline for Homotopy groups of spaces of embeddings
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
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| May 29, 2014 at 0:42 | comment | added | John Klein | Yes. Sorry. I just emailed you the link. | |
| May 29, 2014 at 0:38 | comment | added | John Klein | As far as the concordance stable range goes: fix an embedding $M \to N$. Then we need to look at the connectivity of the stabilization map $CE(M,N) \to CE(M \times I,N\times I)$. I don't recall the exact numbers, but Tom does. (I think the map is approximately $(n-m)$-connected.) | |
| May 29, 2014 at 0:29 | comment | added | Igor Belegradek | Yes, I would appreciate a copy. | |
| May 29, 2014 at 0:16 | comment | added | John Klein | Igor, the joint paper that Tom alludes to below is almost done ("Multiple disjunction for spaces of smooth embeddings"). This paper is the second and last step of the program. I can send you a preliminary version if you wish to see it. | |
| May 29, 2014 at 0:04 | comment | added | Igor Belegradek | I searched for the strategy 2) in the literature and the only source I found was "Multiple disjunction for spaces of Poincaré embeddings", and it seems to only cover the first step; in fact, I hardly ever see any other use of "the space of Poincare embeddings". Is this where things stand, or am I not looking hard enough? | |
| May 28, 2014 at 17:06 | comment | added | Igor Belegradek | I really like the strategy in 2) even though it will take me some time to digest it and see if I can make it work. One concern that I have is about the concordance stable range: does it mean that $k$ must be small in computing $\pi_k(\mathrm{Emb}(M,N))$? If so, would not then the usual (Dax-Haefliger) metastable results kick in? What happens to the strategy in the metastable range? | |
| May 28, 2014 at 3:05 | history | edited | John Klein | CC BY-SA 3.0 |
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| May 28, 2014 at 1:59 | comment | added | John Klein | Yes, it does require codimension $\ge 3$. | |
| May 28, 2014 at 1:38 | comment | added | Igor Belegradek | Thank you! Doesn't contractibility of the homotopy fiber of $E^{\mathrm{pd}}(M,N)\to F(M,N)$ require codimension $\ge 3$? | |
| May 28, 2014 at 1:24 | history | edited | John Klein | CC BY-SA 3.0 |
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| May 27, 2014 at 23:07 | history | edited | John Klein | CC BY-SA 3.0 |
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| May 27, 2014 at 23:02 | history | edited | John Klein | CC BY-SA 3.0 |
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| May 27, 2014 at 22:54 | history | edited | John Klein | CC BY-SA 3.0 |
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| May 27, 2014 at 22:37 | history | edited | John Klein | CC BY-SA 3.0 |
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| May 27, 2014 at 22:28 | history | answered | John Klein | CC BY-SA 3.0 |