Timeline for Codimension zero embeddings and maps with small fibers
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
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| Dec 10 at 2:04 | history | edited | LSpice | CC BY-SA 4.0 |
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| Dec 9 at 20:51 | history | edited | Matthew Kvalheim | CC BY-SA 4.0 |
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| Dec 9 at 20:42 | history | edited | Matthew Kvalheim | CC BY-SA 4.0 |
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| Dec 9 at 16:00 | vote | accept | Matthew Kvalheim | ||
| Dec 9 at 4:02 | history | became hot network question | |||
| Dec 9 at 0:22 | answer | added | alesia | timeline score: 6 | |
| Dec 8 at 23:11 | comment | added | Ryan Budney | Thanks, I erased my most recent comment as your edits made them irrellevant. | |
| Dec 8 at 23:09 | comment | added | Matthew Kvalheim | @RyanBudney sorry, I see now that the original wording of my question’s second paragraph was unclear. I edited it and hope it’s clearer now. | |
| Dec 8 at 23:07 | history | edited | Matthew Kvalheim | CC BY-SA 4.0 |
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| Dec 8 at 20:48 | comment | added | Matthew Kvalheim | @MoisheKohan I had started to do so, but have not yet made much progress. | |
| Dec 8 at 20:39 | comment | added | Moishe Kohan | Did you check if Ferry's arguments from his 1979 AJM paper on $\epsilon$-homeomorphisms apply in your situation? (There is no formal application, of course.) | |
| Dec 8 at 20:20 | history | edited | Matthew Kvalheim | CC BY-SA 4.0 |
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| Dec 8 at 20:17 | comment | added | Matthew Kvalheim | @RyanBudney and no, I do not think I am asking about an isotopy class of an embedding. In my question, it is not allowed for there to exist any embeddings at all of $M$ into $N$. | |
| Dec 8 at 20:15 | comment | added | Matthew Kvalheim | @RyanBudney The Riemannian metric on $M$ induces a distance function, with respect to which we can define the diameter of an arbitrary subset. I am asking whether there exist $M$, $N$ such that $M$ does not embed in $N$ but there exists a sequence of continuous maps $f_k : M\to N$ such that $\sup_{n\in N} \text{diam} f_k^{-1}(n) \to 0$ as $k\to \infty$. For example, by an argument using top degree homology, this situation cannot occur if $N$ is an open manifold and $M$ is not. I think my question is related to 1979 work of Chapman and Ferry, but I do not see how to answer my question. | |
| Dec 8 at 18:36 | comment | added | Ryan Budney | If the fibers aren't points or empty, what does it mean for the fibers to be arbitrarily small? I mean, if they're not empty they have some fixed diameter and you wouldn't be able to make $\epsilon$ smaller than that. Are you talking about in an isotopy class of an embedding? | |
| Dec 8 at 16:45 | history | edited | Matthew Kvalheim | CC BY-SA 4.0 |
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| Dec 8 at 16:16 | history | asked | Matthew Kvalheim | CC BY-SA 4.0 |