Published in Journal of Gökova Geometry Topology, Volume 8 (2014)
Title On power subgroups of mapping class groups
Author Louis Funar
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.
Keywords Mapping class group, Dehn twist, power subgroup, symplectic group
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Submitted: Jun 20, 2014
Accepted: Nov 15, 2014
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