Turkish Journal of Mathematics
Abstract
For every positive integer n, we exhibit a cofinite subgroup \Gamma_n of the mapping class group of a surface of genus at most two such that \Gamma_n admits an epimorphism onto a free group of rank n. We conclude that H^1 (\Gamma_n; {\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 \Gamma_n 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 (or a torus) such that it is not the restriction of an endomorphism of the whole group.
DOI
-
First Page
115
Last Page
124
Recommended Citation
KORKMAZ, M (2003). On cofinite subgroups of mapping class groups. Turkish Journal of Mathematics 27 (1): 115-124. https://doi.org/-
