||Journal of Gökova Geometry Topology, Volume 8 (2014)|
||On power subgroups of mapping class groups|
In the first part of this paper we
prove that the mapping class subgroups generated by the
D-th powers of Dehn twists (with D ≥ 2) along a sparse
collection of simple closed curves on an orientable
surface are right angled Artin groups.
The second part is devoted to power quotients,
i.e., quotients by the normal subgroup generated
by the D-th powers of all elements of the mapping class groups.
We show first that for infinitely
many values of D, the power quotient groups are non-trivial.
On the other hand, if 4g+2 does not divide
D then the associated power quotient of the mapping class group of
the genus g ≥ 3 closed surface is trivial.
Eventually, an elementary argument shows that
in genus 2 there are infinitely many power quotients
which are infinite torsion groups.
||Mapping class group, Dehn twist, power subgroup,
|Submitted: ||Jun 20, 2014|
|Accepted: ||Nov 15, 2014|
2014 Journal main page|
Last updated: January 2015
Web address: GokovaGT.org/journal/2014