Timeline for Fundamental group of punctured simply connected subset of $\mathbb{R}^2$
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 17, 2019 at 21:20 | vote | accept | Thomas Browning | ||
| Dec 17, 2019 at 3:49 | answer | added | George Lowther | timeline score: 6 | |
| Dec 17, 2019 at 1:37 | history | edited | Thomas Browning | CC BY-SA 4.0 |
added 85 characters in body
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| Dec 17, 2019 at 0:20 | comment | added | YCor | You might also mentioned the significant feedback you had on MathSE, notably that the result holds when $S$ is compact (and hence, more generally when every compact subset of $S$ is contained in a simply connected compact subset). | |
| Dec 16, 2019 at 21:10 | answer | added | Jeremy Brazas | timeline score: 3 | |
| Dec 16, 2019 at 19:13 | comment | added | Exit path | If the space is a connected CW complex it should be true. Since it’s simply connected, it’s weakly contractible. If it’s a CW complex then it’s contractible. By your assumption that it contains an open ball, the space has a $2$-cell, so the inclusion of the $2$-cell into your space is a homotopy equivalence. Removing the point in the interior of the $2$-cell should induce a homotopy equivalence of the punctured space with $S^1$ | |
| Dec 16, 2019 at 18:45 | history | asked | Thomas Browning | CC BY-SA 4.0 |