On cofinite subgroups of mapping class groups
| dc.creator | Korkmaz, Mustafa | |
| dc.date | 2003-07-09 | |
| dc.date.accessioned | 2026-07-07T04:59:31Z | |
| dc.date.available | 2026-07-07T04:59:31Z | |
| dc.description | For 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.description | 9 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/math/0307110 | |
| dc.identifier | http://arxiv.org/abs/math/0307110 | |
| dc.identifier | Proceedings of 9th Gokova Geometry-Topology Conference,Turkish Journal of Mathematics 27, no:1. (2003), 115-123 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68014 | |
| dc.subject | Geometric Topology | |
| dc.subject | Group Theory | |
| dc.title | On cofinite subgroups of mapping class groups | |
| dc.type | text |