On power subgroups of mapping class groups

Details On power subgroups of mapping class groups On power subgroups of mapping class groups

2009-10-08

arxiv.org/abs/0910.1493v2

Mathematics

Geometric Topology

15p., 2 figures, section 3.1 rewritten

Scientific paper

In the first part of this paper we prove that the mapping class subgroups generated by the $D$-th powers of Dehn twists (with $D\geq 2$) along a sparse collection of simple closed curves on a 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 group. We show first that for infinitely many $D$ 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 $g$ closed surface is trivial. Eventually, an elementary argument shows that in genus 2 there are infinitely many power quotients which are infinite torsion groups.

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