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Aug 9, 2010 at 22:50 comment added Andy Putman Yes. To get from there to the unordered situation, just mod out by the obvious S_n action.
Aug 9, 2010 at 22:35 comment added HYYY Dear Andy, the mapping class group in Birman exact sequence should be pure mapping class group,i.e.,it fixes each puncture individually, then the corresponding moduli space should be the moduli space of Riemann surface with ordered puncture right?
Aug 8, 2010 at 12:35 vote accept HYYY
Aug 8, 2010 at 4:37 history answered Andy Putman CC BY-SA 2.5