Curve complexes and finite index subgroups of mapping class groups

Details Curve complexes and finite index subgroups of mapping class groups Curve complexes and finite index subgroups of mapping class groups

2005-04-15

arxiv.org/abs/math/0504328v2

Geometriae Dedicata, 118, (2006), 71-85

Mathematics

Geometric Topology

17 pages, 1 figure, minor mistake in closed genus 2 case corrected, references updated

Scientific paper

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).

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