Timeline for Classification of surfaces composed of circles
Current License: CC BY-SA 3.0
23 events
| when toggle format | what | by | license | comment | |
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| Jun 21, 2017 at 11:35 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
deleted 32 characters in body; edited tags
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| Nov 28, 2010 at 15:35 | history | edited | Joseph O'Rourke | CC BY-SA 2.5 |
Addendum on topological circles.
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| Nov 27, 2010 at 19:41 | answer | added | Bill Thurston | timeline score: 14 | |
| Nov 27, 2010 at 14:48 | history | edited | Joseph O'Rourke | CC BY-SA 2.5 |
added 10 characters in body
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| Nov 27, 2010 at 13:31 | history | edited | Joseph O'Rourke | CC BY-SA 2.5 |
added 31 characters in body
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| Nov 27, 2010 at 12:34 | history | edited | Joseph O'Rourke | CC BY-SA 2.5 |
Cristi's wormhole added to list.
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| Nov 27, 2010 at 12:17 | history | edited | Joseph O'Rourke | CC BY-SA 2.5 |
added 9 characters in body
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| Nov 27, 2010 at 12:11 | comment | added | Joseph O'Rourke | @Charles: Excellent point, definition revised as you suggest (which is what I intended). Thanks! | |
| Nov 27, 2010 at 12:10 | comment | added | Joseph O'Rourke | @Mark: Yes! I think you are right: the Klein bottle! | |
| Nov 27, 2010 at 12:10 | comment | added | Joseph O'Rourke | @J.M.: That lemniscate tube would not be embedded. But a candidate if generalized to immersions. | |
| Nov 27, 2010 at 12:08 | history | edited | Joseph O'Rourke | CC BY-SA 2.5 |
Edits to clarify according to comments.
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| Nov 27, 2010 at 11:01 | answer | added | Cristi Stoica | timeline score: 6 | |
| Nov 27, 2010 at 9:41 | comment | added | Mark Grant | Regarding your relaxation (a): would the Klein bottle count? It fibres over $S^1$ with fibre $S^1$. | |
| Nov 27, 2010 at 9:38 | answer | added | Spencer | timeline score: 3 | |
| Nov 27, 2010 at 8:30 | comment | added | sleepless in beantown | @Charles-Siegel, if you look at the Villarceau circles referenced below by Michael Hardy, there are also two more (non-obvious) circles that also going through each point on a torus. There's an excellent image at www-fourier.ujf-grenoble.fr/~bkloeckn/images/villarceau.png on Benoît Kloeckner's web site. | |
| Nov 27, 2010 at 8:23 | answer | added | sleepless in beantown | timeline score: 1 | |
| Nov 27, 2010 at 3:31 | comment | added | J. M. isn't a mathematician | The tube formed from a lemniscate does not count as a genus-2 surface? | |
| Nov 27, 2010 at 2:56 | comment | added | Charles Siegel | You definition of a hoop surface doesn't imply what you say it does. You mention that every point lies on a unique circle, which is false, for instance, on the torus, each point lies on two obvious circles, a vertical and a horizontal one. You could fix this by choosing a circling, and saying that it lies on a unique circle in it. | |
| Nov 27, 2010 at 2:04 | answer | added | Michael Hardy | timeline score: 2 | |
| Nov 27, 2010 at 2:04 | comment | added | Joseph O'Rourke | @J.C.: Good point! I was struggling to describe those surfaces succinctly. They are not planar. But you are right, I shouldn't mention homeomorphism, for just the reason you articulate. | |
| Nov 27, 2010 at 1:56 | comment | added | J.C. Ottem | Why do you bring homeomorphism into the picture? The square is homeomorphic to a disk, but is not covered by circles in the sense you want.. | |
| Nov 27, 2010 at 1:39 | answer | added | BMann | timeline score: 4 | |
| Nov 27, 2010 at 0:05 | history | asked | Joseph O'Rourke | CC BY-SA 2.5 |
