Timeline for Triangulating surfaces
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Aug 4, 2020 at 19:44 | comment | added | Andy Putman | @AllenHatcher: I think I suggested this to you a while ago, but I'll repeat it -- I think this note is a very valuable contribution to the literature, and you should consider submitting it to a journal that publishes semi-expository papers (e.g. L'Enseignment Math). | |
| Aug 4, 2020 at 19:12 | comment | added | Allen Hatcher | @M.Winter: Fixed the link, added the title. | |
| Aug 4, 2020 at 19:09 | history | edited | Allen Hatcher | CC BY-SA 4.0 |
updated link
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| Aug 4, 2020 at 12:51 | comment | added | M. Winter | The link in the answer seems to be down. Hopefully someone can fix this. In general, for such situations, it would be better to have the title of the paper included in the answer, so that one can put it into google. | |
| Mar 15, 2017 at 3:25 | comment | added | Allen Hatcher | @Marvin Jay Greenberg: The Osgood reference Siebenmann gives is W. F. Osgood, “On the transformation of the boundary in the case of conformal mapping”, Bull. Amer. Math. Soc. vol. 9 no. 5 (1903), 233–235. This announces some technical results which Osgood says allow him to prove that, given a Jordan curve C, there is a conformal homeomorphism from the interior of C onto the interior of the unit circle that extends continuously to C. He doesn't seem to say the extension is a homeomorphism from C to the circle. This is three years before Schoenflies' paper in the 1906 Math. Annalen. | |
| Mar 14, 2017 at 22:26 | comment | added | Marvin Jay Greenberg | Abstract for Siebenmann: The very first unknotting theorem of a purely topological character established that every compact subset of the Euclidean plane homeomorphic to a circle can be moved onto a round circle by a globally defined self-homeomorphism of the plane. This difficult hundred-year-old theorem is here celebrated with a partly new elementary proof, and a first but tentative account of its history. Some quite fundamental corollaries of the proof are sketched, and some generalizations are mentioned. I currently can't access this and I wonder what Osgood had to do with the theorem. | |
| Mar 14, 2017 at 22:16 | comment | added | Marvin Jay Greenberg | "The Osgood-Schoenflies theorem revisited" L C Siebenmann © 2005 Russian Academy of Sciences, (DoM) and London Mathematical Society, Turpion Ltd Russian Mathematical Surveys, Volume 60, Number 4 Errata to the paper by L C Siebenmann "The Osgood-Schoenflies theorem revisited" Russian Mathematical Surveys, Volume 60 (2005), Number 4, Pages 645-672 | |
| Jul 13, 2014 at 17:31 | comment | added | Leonard | @Allen Hatcher: Hi Professor Hatcher. What I gather from your response is that it’s wrong to think that the Jordan-Schoenflies Theorem is solely responsible for the triangulability of surfaces — topological $ 3 $-manifolds are triangulable, yet the Jordan-Schoenflies Theorem doesn’t hold in dimension $ 3 $. It thus seems that Kirby’s torus trick is the correct way of approaching the problem of the triangulability of topological manifolds of dimension $ 2 $ or $ 3 $. However, I don’t see why the trick fails in higher dimensions, so I’m wondering if you can say something about it. Thanks! | |
| Dec 13, 2013 at 16:52 | comment | added | Andy Putman | This proof is really great. I probably wouldn't try to teach it to undergraduates, but for people with a little sophistication it is clearly the "right" proof. Thanks for writing it up! | |
| Dec 13, 2013 at 16:39 | vote | accept | Andy Putman | ||
| Dec 13, 2013 at 16:33 | history | answered | Allen Hatcher | CC BY-SA 3.0 |