Curve complexes and finite index subgroups of mapping class groups
Geometric Topology
2008-11-15 v2 Group Theory
Abstract
Let Mod(S) be the extended mapping class group of a surface S. For S the twice-punctured torus, we show that there exists an isomorphism of finite index subgroups of Mod(S) which is not the restriction of an inner automorphism. For S a torus with at least three punctures, we show that every injection of a finite index subgroup of Mod(S) into Mod(S) is the restriction of an inner automorphism; this completes a program begun by Irmak. For all of the above surfaces, we establish the co-Hopf property for finite index subgroups of Mod(S).
Cite
@article{arxiv.math/0504328,
title = {Curve complexes and finite index subgroups of mapping class groups},
author = {Jason Behrstock and Dan Margalit},
journal= {arXiv preprint arXiv:math/0504328},
year = {2008}
}
Comments
17 pages, 1 figure, minor mistake in closed genus 2 case corrected, references updated