Timeline for Piecewise linear Poincaré conjecture
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 26, 2019 at 19:05 | vote | accept | Stefan Friedl | ||
| Aug 25, 2019 at 13:57 | answer | added | Igor Belegradek | timeline score: 11 | |
| Aug 25, 2019 at 7:25 | comment | added | Stefan Friedl | I also had a look at Stallings notes, but it is not clear how it helps. I guess many of these arguments are only comprehensible if one is immersed in the PL-language, which people were in the 60s. This teaches us again the lesson that results should be written up in such a way that they are comprehensible by future generations who might have a very different background. | |
| Aug 25, 2019 at 3:31 | comment | added | Igor Belegradek | I don't think Kirby-Siebenmann's results are relevant here. As Rudyak says before theorem 3.12, everything was settled in the 60s. The details are not on my fingertips though. I briefly looked in Stallings' notes and could not immediately see how to use them to adapt Smale's argument to the PL setting. | |
| Aug 24, 2019 at 20:21 | comment | added | Stefan Friedl | Yes, that's a good answer. It does follow indeed from Kirby-Siebenmann. Incidentally, it also follows from K-S that every topological manifold that is h.e. to $S^n$ is homeomorphic to $S^n$, which I guess does not follow from any of the original approaches. This still begs the question though, whether K-S is necessary. Zeeman seems to suggest that it should have been known by the early 1960's. | |
| Aug 24, 2019 at 13:12 | comment | added | Igor Belegradek | See theorem 3.12 in arxiv.org/abs/math/0105047 and references therein. | |
| Aug 24, 2019 at 11:38 | history | edited | YCor | CC BY-SA 4.0 |
added links, formatting, added tag
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| Aug 24, 2019 at 11:11 | history | asked | Stefan Friedl | CC BY-SA 4.0 |