Timeline for Topological invariants of toroidal orbifolds
Current License: CC BY-SA 3.0
5 events
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| Feb 7, 2014 at 6:21 | comment | added | Neil Hoffman | @Gian Actually, $T^2/(\mathbb{Z}/3\mathbb{Z} \times \mathbb{Z}/3\mathbb{Z})$ could be a compact orbifold. In fact, the torus covers itself via such deck transformations. My answer above gives all of the possible orbifolds of the form you wanted together with a realization. However, other realizations exist - $S^2(2,2,2,2)$ can cover itself via an order 2 covering map, and so it can also be realized as $T^2/(\mathbb{Z}/3\mathbb{Z} \times \mathbb{Z}/3\mathbb{Z})$. | |
| Feb 5, 2014 at 20:04 | history | edited | Neil Hoffman | CC BY-SA 3.0 |
fixed a small typo in the quotient group of RP^2(2,2)
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| Feb 5, 2014 at 18:21 | vote | accept | Gian | ||
| Feb 5, 2014 at 18:20 | comment | added | Gian | Very nice answer, thanks a lot! Just a very brief stupid question: what if I consider $T^2/Z/(3Z \times 3Z)$ or $T^2/Z/(4Z \times 4Z)$? They are not compact orbifolds, right? But in this case, do they have any mathematical meaning? | |
| Feb 3, 2014 at 23:33 | history | answered | Neil Hoffman | CC BY-SA 3.0 |