Timeline for Surgery along an arc connecting the components of a $2$-component link gives the unknot
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Jul 30, 2015 at 18:12 | comment | added | Jim Conant | Oh oops. That's what happens when I comment when I first get up in the morning. 2-spheres, 3-spheres same difference. | |
| Jul 30, 2015 at 17:41 | comment | added | Ian Agol | Hey Jim - the paper has nothing to do with Schoenfies - it's about 2-spheres embedded in $\mathbb{R}^4$ with 4 critical points. Saying such a sphere is standard is equivalent to saying that any band sum of the 2-component unlink which gives the unknot is standard. Scharlemann proves this actually for split links. A simpler proof was found later by Thompson. dx.doi.org/10.1016/0040-9383(87)90060-7 | |
| Jul 30, 2015 at 14:11 | comment | added | Jim Conant | The funny thing is that I read Scharlemann's paper in grad school, and you were in the audience when I presented it in the topology seminar! Are you saying that a band sum of a nontrivial split link which is the unknot would give a counterexample to the 4D Schönflies conjecture? | |
| Jul 30, 2015 at 4:28 | history | edited | Ian Agol | CC BY-SA 3.0 |
added 368 characters in body
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| Jul 30, 2015 at 4:15 | history | answered | Ian Agol | CC BY-SA 3.0 |