Timeline for Covering spaces of surfaces
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Aug 15, 2012 at 20:44 | comment | added | Misha | @algori: I meant an easier argument: Every genus $r$ surface group maps onto a rank $r$ free group, which then maps onto an $r$-generated finite group. For simple groups, then use the fact that they are all 2-generated. | |
| Aug 15, 2012 at 20:33 | comment | added | algori | Misha -- re your first statement: yes, one can let a finite group act freely e.g. on the 1-skeleton of the simplex whose vertices correspond to the elements of the group, and then construct a surface as above. | |
| Aug 15, 2012 at 20:08 | comment | added | Misha | One should also note that, of course, every finite group appears as the covering group for some covering between surfaces. Say, every finite simple group appears as a covering group over genus 2 surface. | |
| Aug 15, 2012 at 18:53 | history | edited | algori | CC BY-SA 3.0 |
specified the angles; fixed a typo
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| Aug 15, 2012 at 16:39 | history | answered | algori | CC BY-SA 3.0 |