Timeline for Condition on a Lie groupoid to be represented by manifold/group or an action groupoid
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
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| Feb 17, 2019 at 18:26 | comment | added | Praphulla Koushik | @AndréHenriques I hope some one (including me :)) can achieve that some day.. I will read what is written in your thesis first and then ask you more questions :) :) | |
| Feb 17, 2019 at 18:20 | comment | added | André Henriques | @Prapulla Koushik. Yes, despite what is written in that section, the conjecture is still open. I have spent a large amount of time and energy in the years following my PhD trying to complete the proof. But I have not succeeded. It's now time for others to try to do what I have failed to achieve. (And I'm of course happy to offer advice to whoever wishes to try) | |
| Feb 17, 2019 at 16:15 | history | edited | Praphulla Koushik | CC BY-SA 4.0 |
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| Feb 17, 2019 at 13:43 | comment | added | Praphulla Koushik | @S.Carnahan :O current status does not mean just knowing if it is open or not... I was expecting something about if he knows any one working on that or some related information... I did not feel good that you have deleted my comment... But, that is ok.. I do not know if there is any other reason, so I do not want to take it personally :) :) | |
| Feb 17, 2019 at 13:38 | comment | added | S. Carnahan♦ | @PraphullaKoushik I have deleted your request for current status, because it is already answered in André's comment. | |
| Feb 17, 2019 at 6:10 | comment | added | Praphulla Koushik | @S.Carnahan you mean “I have some ideas on how to fix the whole thing, but if you're looking for a rigorous proof, you'll be disappointed” and “It's mostly correct except for a couple of places where there are problems with the small object argument. ”?.. I understand.. I did not read the warning :) | |
| Feb 17, 2019 at 6:08 | comment | added | S. Carnahan♦ | @PraphullaKoushik Did you read the warning he wrote on the page he linked? | |
| Feb 17, 2019 at 5:55 | comment | added | Praphulla Koushik | @AndréHenriques you said in page 93 before section $6.3$ “So we have also proven that every compact orbifold is the quotient of a compact manifold by a compact Lie group.” You are saying the conjecture is still open.. I don’t know what is that I am misunderstanding... by compact Orbifold you mean a proper etale Lie groupoid whose vase space is compact.. Is that it? | |
| Feb 17, 2019 at 5:48 | comment | added | David Roberts♦ | I would take the traditional definition to include the effectivity condition, whether one uses spaces with orbifold charts, or Lie groupoids. | |
| Feb 17, 2019 at 3:54 | comment | added | Praphulla Koushik | @DavidRoberts that is by mistake. I wan to say proper and injective, not proper and closed... :) I do not know what Is traditional definition but I read Orbifold is Proper etale lie groupoid.. By traditional definition you mean orbifold as topological space with extra properties?? | |
| Feb 17, 2019 at 3:53 | history | edited | Praphulla Koushik | CC BY-SA 4.0 |
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| Feb 17, 2019 at 1:07 | comment | added | David Roberts♦ | "is sufficient to confirm" <--- I guess you are missing "is injective" just before this phrase. Also, "proper" includes the condition/implies the map is closed (depending on which of the equivalent def'ns of proper you take) | |
| Feb 17, 2019 at 1:06 | comment | added | David Roberts♦ | @André I guess by orbifold you mean a proper étale Lie groupoid, as opposed to the traditional definition? | |
| Feb 16, 2019 at 23:41 | comment | added | André Henriques | I have conjectured a long time ago that every compact orbifold is (Morita equivalent to) a quotient of a manifold by a compact Lie group. See my PhD thesis available at andreghenriques.com/thesiswarning.html. I strongly believe that this conjecture is true. But my understanding is that this conjecture is still open. Note that, for effective orbifolds, the statement is very easy to prove as the total space of the frame bundle is then a manifold. | |
| Feb 16, 2019 at 22:22 | history | asked | Praphulla Koushik | CC BY-SA 4.0 |