Timeline for Fundamental group of $\mathbb{R}^3-F$ where $F\subseteq \mathbb{R}\times \{0\} \times \{0\}$
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 31, 2014 at 5:48 | vote | accept | Oliver Straser | ||
| Jul 31, 2014 at 1:06 | answer | added | S. Carnahan♦ | timeline score: 7 | |
| Jul 30, 2014 at 14:42 | comment | added | Daniel Valenzuela | I guess you can freely homotop an element in $[S^1,\mathbb R^3 -(Z-F)]$ parallel to $Z$ into an orthogonal plane of $Z$ based at a point of $F$. You can easily contract it in this plane to a point without problems. Hence the statement. | |
| Jul 30, 2014 at 14:18 | comment | added | ThiKu | The same should hold true for any loop in $R^3-Z$, just that in this case the disks won't be embedded anymore. | |
| Jul 30, 2014 at 14:17 | comment | added | ThiKu | I think so. Look at a loop representing the generator of $\pi_1(\R^3-Z)$. As soon as you remove at least one point from Z, then this loop will bound some embedded disk. | |
| Jul 30, 2014 at 13:53 | history | asked | Oliver Straser | CC BY-SA 3.0 |