On cofinite subgroups of mapping class groups

Authors : Mustafa KORKMAZ

Pages : 115-124

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :For every positive integer n, we exhibit a cofinite subgroup Gn of the mapping class group of a surface of genus at most two such that Gn admits an epimorphism onto a free group of rank n. We conclude that H1 insert ignore into journalissuearticles values(Gn; {\mathbb Z}); has rank at least n and the dimension of the second bounded cohomology of each of these mapping class groups is the cardinality of the continuum. In the case of genus two, the groups Gn can be chosen not to contain the Torelli group. Similarly for hyperelliptic mapping class groups. We also exhibit an automorphism of a subgroup of finite index in the mapping class group of a sphere with four punctures insert ignore into journalissuearticles values(or a torus); such that it is not the restriction of an endomorphism of the whole group.
Keywords : Turk J Math, 27, 2003, , 115 124 Turk J Math, vol 27, iss 1