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, MUSTAFA (2003) "On cofinite subgroups of mapping class groups," Turkish Journal of Mathematics: Vol. 27: No. 1, Article 6. Available at: https://journals.tubitak.gov.tr/math/vol27/iss1/6
