On cofinite subgroups of mapping class groups

dc.creatorKorkmaz, Mustafa
dc.date2003-07-09
dc.date.accessioned2026-07-07T04:59:31Z
dc.date.available2026-07-07T04:59:31Z
dc.descriptionFor any positive integer $n$, we exhibit a cofinite subgroup $Γ_n$ of the mapping class group of a surface of genus at most two such that $Γ_n$ admits an epimorphism onto a free group of rank $n$. We conclude that $H^1(Γ_n;\Z)$ 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 $Γ_n$ 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.
dc.description9 pages, 1 figure
dc.identifierhttps://arxiv.org/abs/math/0307110
dc.identifierhttp://arxiv.org/abs/math/0307110
dc.identifierProceedings of 9th Gokova Geometry-Topology Conference,Turkish Journal of Mathematics 27, no:1. (2003), 115-123
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/68014
dc.subjectGeometric Topology
dc.subjectGroup Theory
dc.titleOn cofinite subgroups of mapping class groups
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