Timeline for Is a non-compact Riemann surface an open subset of a compact one ?
Current License: CC BY-SA 2.5
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| Mar 20, 2011 at 16:23 | comment | added | André Henriques | @evgeniamerkulova: The surface you describe has genus zero. The genus of a non-compact Riemann surface is the maximal $g$ so that $\Sigma_g$ minus one point embeds into the Riemann surface (where $\Sigma_g$ is a compact Riemann surface of genus $g$). @unknowngoogle: You could modify your question by adding the condition that the surface you consider has finite genus (where genus is defined as above). | |
| Mar 20, 2011 at 8:15 | comment | added | evgeniamerkulova | I do not understand. what is genus of $\mathbb C \setminus K$ for $K$ is Cantor set in $[0,1]$ ? | |
| Mar 20, 2011 at 1:16 | vote | accept | Qfwfq | ||
| Mar 20, 2011 at 13:53 | |||||
| Mar 20, 2011 at 1:16 | comment | added | Qfwfq | Oh, yes! I knew there were problems in compactifying: perhaps I already read this (or even asked in a comment!) on MO, but I wasn't able to remember the point. Thanks; now I think the question can be closed. | |
| Mar 20, 2011 at 1:13 | history | answered | André Henriques | CC BY-SA 2.5 |