Generating the mapping class group of a punctured surface by involutions
| dc.creator | Monden, Naoyuki | |
| dc.date | 2008-07-06 | |
| dc.date | 2008-09-01 | |
| dc.date.accessioned | 2026-07-07T09:59:22Z | |
| dc.date.available | 2026-07-07T09:59:22Z | |
| dc.description | Let $Σ_{g,b}$ denote a closed orientable surface of genus $g$ with $b$ punctures and let $\rm Mod(Σ_{\textit{g,b}})$ denote its mapping class group. In [Luo] Luo proved that if the genus is at least 3, $\rm Mod(Σ_{\textit{g,b}})$ is generated by involutions. He also asked if there exists a universal upper bound, independent of genus and the number of punctures, for the number of torsion elements/involutions needed to generate $\rm Mod(Σ_{\textit{g,b}})$. Brendle and Farb [BF] gave an answer in the case of $g\geq 3, b=0$ and $g\geq 4, b=1$, by describing a generating set consisting of 6 involutions. Kassabov showed that for every $b$ $\rm Mod(Σ_{\textit{g,b}})$ can be generated by 4 involutions if $g\geq 8$, 5 involutions if $g\geq 6$ and 6 involutions if $g\geq 4$. We proved that for every $b$ $\rm Mod(Σ_{\textit{g,b}})$ can be generated by 4 involutions if $g\geq 7$ and 5 involutions if $g\geq 5$. | |
| dc.description | 18 pages, 11 figures. E-mail address is changed | |
| dc.identifier | https://arxiv.org/abs/0807.0916 | |
| dc.identifier | http://arxiv.org/abs/0807.0916 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/167997 | |
| dc.subject | Geometric Topology | |
| dc.subject | Group Theory | |
| dc.subject | 20F65, 57M07 | |
| dc.title | Generating the mapping class group of a punctured surface by involutions | |
| dc.type | text |