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Sep 27, 2018 at 19:15 comment added Andy Putman @PaulPlummer: That is correct.
Sep 27, 2018 at 16:43 comment added user35370 I guess it is also because abelian subgroups, up to finite index, are generated by elements supported on disjoint subsurfaces. I think this is done in Abelian and solvable subgroups of the mapping class group by Birman, Lubotzky, McCarthy.
Sep 27, 2018 at 16:11 comment added user35370 Could you say a bit as to why their paper shows that? Skimming the paper they only specifically mention cyclic subgroups are undistorted.
Jul 12, 2014 at 18:50 vote accept Anonymous
Jun 30, 2014 at 2:31 history answered Andy Putman CC BY-SA 3.0