Timeline for Can we foliate the punctured space by tori?
Current License: CC BY-SA 3.0
18 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 10, 2013 at 17:52 | history | edited | Ali Taghavi | CC BY-SA 3.0 |
added 13 characters in body
|
| Dec 7, 2013 at 18:16 | vote | accept | Ali Taghavi | ||
| Dec 6, 2013 at 22:09 | comment | added | JHM | We would know that the base space must be noncompact, since the total space of a fibration having compact fibres over a compact base is compact. And the only noncompact smooth (connected) $1$-mfld is our very favourite real line. | |
| Dec 6, 2013 at 22:06 | answer | added | JHM | timeline score: 3 | |
| Dec 6, 2013 at 5:34 | answer | added | Bin Yu | timeline score: 1 | |
| Dec 6, 2013 at 0:17 | comment | added | Ali Taghavi | a good question about R2 plane. But just a question :why long exact homotopy sequence implies that there is no a fibration,We do not know what is the base space | |
| Dec 5, 2013 at 14:09 | comment | added | JHM | A related (and possibly easier) question would be to show that R^3-0 is not foliated by R^2-planes, here seeing R^2 as the universal cover of T^2, and likewise can we foliate by higher genus (possibly open) surfaces? I expect `no', but not exactly sure why. | |
| Dec 5, 2013 at 13:56 | comment | added | JHM | @AliTaghavi: I really like your question and i don't have an answer, but i'm thinking about it. What is obvious (via the long exact homotopy sequence) is that there is no fibration of $R^3-0$ by tori -- but a foliation is rather far from being a fibration. | |
| Dec 5, 2013 at 13:18 | comment | added | Ali Taghavi | @J.Martel, I agree with you. R^{3}-{0} is foliated by a one parameter familly of 2- spheres. Do you have any Idea on the main question:the foliation of R^3-{0} by torus? Thanks | |
| Dec 5, 2013 at 0:17 | comment | added | JHM | I am not convinced that the vanishing of the euler characteristic is necessary for open 3-manifolds to support a codimension 1 foliation -- it certainly is not necessary for open surfaces. | |
| Dec 4, 2013 at 17:41 | comment | added | ThiKu | The vanishing of the Euler characteristic is a necessary condition for the existence of a codimension 1 foliation, but of course the Euler characteristic of $R^3-0$ does vanish, so this doesn't put an obstacle in this case. | |
| Dec 3, 2013 at 22:00 | history | edited | Ali Taghavi | CC BY-SA 3.0 |
added 141 characters in body
|
| Dec 3, 2013 at 21:44 | history | edited | Ali Taghavi |
edited tags
|
|
| S Dec 3, 2013 at 20:17 | history | suggested | ThiKu | CC BY-SA 3.0 |
Corrected spelling
|
| Dec 3, 2013 at 20:11 | review | Suggested edits | |||
| S Dec 3, 2013 at 20:17 | |||||
| Dec 3, 2013 at 19:25 | history | edited | Ali Taghavi | CC BY-SA 3.0 |
edited body
|
| Dec 3, 2013 at 19:18 | history | edited | Ali Taghavi | CC BY-SA 3.0 |
added 366 characters in body
|
| Dec 3, 2013 at 18:40 | history | asked | Ali Taghavi | CC BY-SA 3.0 |