Timeline for Homeomorphisms of $S^n\times S^1$
Current License: CC BY-SA 3.0
32 events
| when toggle format | what | by | license | comment | |
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| Feb 20, 2017 at 0:00 | answer | added | Ben Wieland | timeline score: 3 | |
| Feb 13, 2017 at 3:05 | comment | added | Ben Wieland | Exotic 7-spheres correspond to exotic diffeomorphisms of the 6-sphere and the 6-disk. For any 6-manifold, the connected sum of the identity with such a diffeomorphism of the disk gives a diffeomorphism of the 6-manifold that might be exotic. In particular, it gives a diffeomorphism of $S^5\times S^1$ that is not pseudo-isotopic to the identity, as detected by its action on appropriate versions of the tangent bundle, those with structure group $G/O$ or $Top/O$. | |
| Feb 7, 2017 at 5:44 | comment | added | olga | Please, explain in details what you mean. What is not tue? what is [X,Y]? | |
| Feb 6, 2017 at 15:29 | comment | added | Ben Wieland | I don't think that this is true in the smooth category. There is a tangential invariant in $[S^n\times S^1,Top/O]=[S^n,Top/O]\oplus[S^1,Top/O]\oplus[S^{n+1},Top/O]$. I think that the last factor is an obstruction and can be realized. | |
| Feb 5, 2017 at 12:29 | history | edited | olga | CC BY-SA 3.0 |
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| Feb 5, 2017 at 2:47 | comment | added | Włodzimierz Holsztyński | The following link (perhaps) will not contribute to answering the Question but may still feel related to the topic: ams.org/journals/proc/1971-027-03/S0002-9939-1971-0271949-X/… | |
| Feb 4, 2017 at 22:41 | comment | added | Włodzimierz Holsztyński | How do I vote for NOT CLOSING this question? | |
| Feb 4, 2017 at 6:11 | history | edited | olga | CC BY-SA 3.0 |
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| Feb 4, 2017 at 5:55 | history | edited | olga | CC BY-SA 3.0 |
added 7 characters in body
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| Feb 3, 2017 at 15:51 | comment | added | Dave Witte Morris | I am confused. The question says the condition on $g$ is only for some $x$, but, in my answer, I assumed you needed the condition for all $x$. Which quantifier is correct? | |
| Feb 3, 2017 at 15:36 | history | rollback | Dave Witte Morris |
Rollback to Revision 3
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| Feb 3, 2017 at 15:34 | history | edited | Dave Witte Morris | CC BY-SA 3.0 |
Comments pointed out that a slightly revised question such as this one is much more interesting.
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| Feb 3, 2017 at 5:34 | answer | added | olga | timeline score: 10 | |
| Feb 1, 2017 at 10:30 | vote | accept | olga | ||
| Feb 5, 2017 at 18:48 | |||||
| Feb 1, 2017 at 10:30 | vote | accept | olga | ||
| Feb 1, 2017 at 10:30 | |||||
| Feb 1, 2017 at 10:30 | vote | accept | olga | ||
| Feb 1, 2017 at 10:30 | |||||
| Feb 1, 2017 at 2:09 | answer | added | Danny Ruberman | timeline score: 15 | |
| Jan 31, 2017 at 21:28 | history | edited | Igor Belegradek | CC BY-SA 3.0 |
added dollar signs in teh title
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| Jan 31, 2017 at 20:41 | comment | added | Denis Nardin | I took the liberty to improve the question. I hope I have not changed the meaning. | |
| Jan 31, 2017 at 20:39 | history | edited | Denis Nardin | CC BY-SA 3.0 |
General corrections to grammar and spelling
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| Jan 31, 2017 at 19:13 | comment | added | Igor Rivin | @TylerLawson In fact, it is virtually certain that the case $n>3$ is completely open. | |
| Jan 31, 2017 at 18:57 | comment | added | olga | I am very sorry if I did not answer to someone. I try to change the situation. I am writing the paper concerning to embedding a cascade to a flow on n-manifold (n>3). This problem is reduced to my question above. Orientation is preserving on $\pi_1$ | |
| Jan 31, 2017 at 18:09 | comment | added | Tyler Lawson | While it may be tempting to be impatient about this question, I don't think it's deserved. Yes, there are a couple of basic obstructions to the existence of such an isotopy (n=1 and the orientation on $\pi_1$, as in the answers so far). Behind those, it seems to me that there is a mathematical question of some real substance, as indicated by the second case in Igor Rivin's answer. There is no need to be dismissive. | |
| Jan 31, 2017 at 17:48 | comment | added | olga | Indeed I interested n>2 | |
| Jan 31, 2017 at 17:47 | answer | added | Dave Witte Morris | timeline score: 5 | |
| Jan 31, 2017 at 17:24 | comment | added | Igor Belegradek | @olga: could you (edit the question to) clarify which $n$ you care about? | |
| Jan 31, 2017 at 17:12 | answer | added | Igor Rivin | timeline score: 18 | |
| Jan 31, 2017 at 17:01 | comment | added | Igor Belegradek | @AnthonyQuas: where do they teach courses on topological isotopies? I do not know the answer to the OP question. If you do, please give a hint. | |
| Jan 31, 2017 at 16:59 | review | Close votes | |||
| Jan 31, 2017 at 21:29 | |||||
| Jan 31, 2017 at 16:32 | comment | added | Anthony Quas | Is this a homework question? | |
| Jan 31, 2017 at 16:20 | review | First posts | |||
| Jan 31, 2017 at 17:28 | |||||
| Jan 31, 2017 at 16:12 | history | asked | olga | CC BY-SA 3.0 |