Timeline for Non-zero winding number on a space curve implies a linked curve in the zero set?
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Apr 19, 2019 at 15:56 | history | edited | Hao Chen | CC BY-SA 4.0 |
deleted 1 character in body
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| Apr 19, 2019 at 14:54 | history | edited | Hao Chen | CC BY-SA 4.0 |
append acknowledgement
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| Apr 18, 2019 at 22:41 | answer | added | Dmitri Panov | timeline score: 2 | |
| Apr 18, 2019 at 16:25 | comment | added | Hao Chen | @OlegEroshkin You are right. As I regard $\mathbb{S}^2$ as compactification of $\mathbb{R}^2$, I mean the winding number of $f(C)$ in $\mathbb{S}^2 \setminus \infty$. It is now clarified in the question. | |
| Apr 18, 2019 at 16:24 | history | edited | Hao Chen | CC BY-SA 4.0 |
clarify the meaning of winding number
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| Apr 18, 2019 at 16:07 | comment | added | Oleg Eroshkin | What is the "winding number" for the loop in $S^2$ around 0? The sphere minus one point is contractible. You need to remove two points to have a nontrivial homotopic invariant. | |
| Apr 18, 2019 at 15:27 | comment | added | Hao Chen | @wojowu this can be fixed by compactify $\mathbb{R}^n$ to $\mathbb{S}^n$. I updated the question accordingly. | |
| Apr 18, 2019 at 15:24 | history | edited | Hao Chen | CC BY-SA 4.0 |
R→S
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| Apr 18, 2019 at 15:20 | comment | added | Wojowu | Let $f$ be the standard projection and $C$ be a flat circle. $f^{-1}(0)$ is a line going through the center of the circle and contains no curve linked to $C$. | |
| Apr 18, 2019 at 13:45 | history | asked | Hao Chen | CC BY-SA 4.0 |