Timeline for A quantity associated with a smooth groupoid
Current License: CC BY-SA 3.0
20 events
| when toggle format | what | by | license | comment | |
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| S Nov 19, 2017 at 4:37 | history | bounty ended | CommunityBot | ||
| S Nov 19, 2017 at 4:37 | history | notice removed | CommunityBot | ||
| Nov 13, 2017 at 20:57 | answer | added | DamienC | timeline score: 2 | |
| Nov 11, 2017 at 16:46 | history | edited | Denis Serre | CC BY-SA 3.0 |
edited title
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| Nov 11, 2017 at 16:36 | answer | added | Nicola Ciccoli | timeline score: 2 | |
| Nov 11, 2017 at 13:43 | comment | added | Ali Taghavi | @NicolaCiccoli In fact transversality implies discrete intersection provided the sum of the codimension would be the dimension of the total space. We loos this situation if we choose $G\times G^0$ as total space. | |
| Nov 11, 2017 at 12:33 | comment | added | Ali Taghavi | @NicolaCiccoli Thank you for your attention to my question and your very interesting suggestion on groupoid action. I think that this quantity vanish for the action of a compact connected group on itself. We consider the graphs as submanifolds of $G\times G$ to have transverslity condition. Otherwise the sum of their dimension is not equal to the total space. For example consider the obvious structure on a group G with $G^0=\{e\}$. | |
| Nov 11, 2017 at 10:00 | comment | added | Nicola Ciccoli | Just one question; why would you like to read graphs of source and target inside $G\times G$ rather than in $G\times G_0$? | |
| Nov 11, 2017 at 8:22 | comment | added | Ali Taghavi | @DavidRoberts Thank you so much for your edit. | |
| Nov 11, 2017 at 8:12 | comment | added | Nicola Ciccoli | I think I'd consider an action groupoid as a test case. There this intersection number should be intuitively related to geometric properties of the set of fixed points, isn't it? | |
| Nov 11, 2017 at 5:47 | comment | added | David Roberts♦ | I fixed some typos for you. | |
| Nov 11, 2017 at 5:47 | history | edited | David Roberts♦ | CC BY-SA 3.0 |
Fixed typos
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| Nov 11, 2017 at 3:55 | comment | added | Ali Taghavi | @bianchira Thank you for your comments. The intersection number can be defined even in the lack of transversality. In fact by a perturbation argument we may assume that they are transversal. Please See Differential topology by M. Hirsch. In fact the intersection number can be defind when two submanifolds are equal.(And this is the base of definition of Euler characteristic of a manifold $M$, $\chi(M)$ is the SELF intersection number of $M$ with itself in $TM$.Moreover since $G^0 \subset G$ then $R,S $ are counted as maps from $G$ to itself. | |
| S Nov 11, 2017 at 2:54 | history | bounty started | Ali Taghavi | ||
| S Nov 11, 2017 at 2:54 | history | notice added | Ali Taghavi | Draw attention | |
| Oct 29, 2017 at 12:44 | history | edited | Ali Taghavi | CC BY-SA 3.0 |
added 2 characters in body
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| Oct 29, 2017 at 12:26 | history | edited | Ali Taghavi | CC BY-SA 3.0 |
added 279 characters in body
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| S Oct 28, 2017 at 21:25 | history | suggested | jeq | CC BY-SA 3.0 |
Corrected typo in title.
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| Oct 28, 2017 at 21:15 | review | Suggested edits | |||
| S Oct 28, 2017 at 21:25 | |||||
| Oct 28, 2017 at 20:51 | history | asked | Ali Taghavi | CC BY-SA 3.0 |