Timeline for compact riemann surface of genus g
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 5, 2010 at 9:14 | comment | added | Pete L. Clark | -1: You have asked a question sufficiently vaguely so that it admits many possible answers, each of which is very well known and well explained in standard texts. Thus you seem to be wasting people's time. | |
| May 5, 2010 at 4:36 | comment | added | S. Carnahan♦ | @Simon: You might want to replace Z with R, and specify that the nonidentity elements are all hyperbolic (i.e., trace squared is strictly greater than 4). | |
| May 5, 2010 at 3:26 | comment | added | Simon Rose | Oh, certainly, but that requires a small amount more work, and realistically should require that you talk about discrete subgroups of $PSL_2(\mathbb{Z})$, and I didn't really want to go there. | |
| May 5, 2010 at 0:26 | answer | added | S. Carnahan♦ | timeline score: 5 | |
| May 4, 2010 at 23:17 | comment | added | Andrea Ferretti | @Simon: your construction will also give you a complex structure, provided your 4g-gon is part of a tiling of the hyperbolic plane (meaning the sides of the tiling are geodesics). | |
| May 4, 2010 at 23:14 | comment | added | Andrea Ferretti | What do you mean by construct? There are various ways either with explicit equations, or as quotients of the disk, or as ramified coverings of $\mathbb{P}^1$... Also, I don't think your question is suitable for MathOverflow, please read the FAQ. | |
| May 4, 2010 at 23:13 | comment | added | Simon Rose | Do you care about complex structure? If not, take a 4g-gon, with edges identified (clockwise) as $a_1 * b_1 * a_1^{-1} b_1^{-1} * \cdots * a_g * b_g * a_g^{-1} b_g^{-1}$, which will give you a topological one... | |
| May 4, 2010 at 23:07 | history | asked | priyanka | CC BY-SA 2.5 |