Timeline for Existence of a non-null-homotopic simple closed curve
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Oct 15, 2015 at 14:10 | vote | accept | smyrlis | ||
| Oct 14, 2015 at 19:45 | comment | added | Włodzimierz Holsztyński | Cont. (finish): The z=0 level curve cannot be contracted because an infinite sequence of the level z=0 points would have to reach the top level z=1 at about the same time during the homotopy. This reaching z=1 would be forced by elementary considerations or by a simple homological argument. | |
| Oct 14, 2015 at 19:39 | comment | added | Włodzimierz Holsztyński | Every simple curve is contained in one of the cones. (The example is fine and elegant, of course). | |
| S Oct 14, 2015 at 15:16 | history | suggested | smyrlis | CC BY-SA 3.0 |
LaTeXified the answer
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| Oct 14, 2015 at 15:08 | comment | added | smyrlis | Your space contains the segment $\{(0,0,t) : t\in[0,1]\}$,which appears to cause some trouble. Why do you need the space to be compact? Could you provide some further explanation or a link? | |
| Oct 14, 2015 at 15:05 | review | Suggested edits | |||
| S Oct 14, 2015 at 15:16 | |||||
| Oct 12, 2015 at 20:54 | history | edited | Paul Fabel | CC BY-SA 3.0 |
A partial positive answer is replaced by a counterexample
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| Oct 12, 2015 at 20:06 | history | edited | Paul Fabel | CC BY-SA 3.0 |
The original post answered a weaker question.
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| Oct 12, 2015 at 20:00 | history | answered | Paul Fabel | CC BY-SA 3.0 |