Timeline for Classification of surfaces composed of circles
Current License: CC BY-SA 2.5
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| Nov 27, 2010 at 1:59 | comment | added | BMann | Ah, I fully understand your question now. My first paragraph is irrelevant. Also, if we allow topological circles, as you suggested in your question, every surface is a circled surface, simply by taking the circles small enough to lie in patches homeomorphic to $\mathbb{R}^2$. For hooped surfaces, I believe the list is pretty much the same, but with the Moebius strip added. | |
| Nov 27, 2010 at 1:45 | comment | added | Joseph O'Rourke | @BMann: By a geometric circle I mean a set in $R^3$ congruent to $x^2 + y^2 = r^2$ in the plane. Nice argument that even topological hoop surfaces cannot have genus more than 1! | |
| Nov 27, 2010 at 1:39 | history | answered | BMann | CC BY-SA 2.5 |