Timeline for Surface separating the boundary of a cylinder
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 15, 2021 at 8:36 | vote | accept | Zhiqiang | ||
| Jun 13, 2021 at 6:12 | comment | added | HJRW | The proof you found is very like one standard topological proof! | |
| Jun 12, 2021 at 22:11 | comment | added | mme | @HJRW Thanks! It seemed obvious something like this was nearby but I wasn't aware of it and struggled to make the algebra argument work. I should read a proof of that lemma. | |
| Jun 12, 2021 at 21:38 | comment | added | HJRW | A little elementary group theory will simplify the argument. Since we know that $\pi_1N$ injects, $\pi_1M$ decomposes as an amalgamated product $\pi_1W_0*_{\pi_1N}\pi_1W_1$. Your argument rediscovers the basic fact (sometimes called Britton’s lemma) that the vertex groups of an amalgamated product inject, which is the fact you needed to finish the proof. | |
| Jun 11, 2021 at 23:38 | history | answered | mme | CC BY-SA 4.0 |