Every mapping class group is generated by 6 involutions
| dc.creator | Brendle, Tara E. | |
| dc.creator | Farb, Benson | |
| dc.date | 2003-07-02 | |
| dc.date | 2004-02-19 | |
| dc.date.accessioned | 2026-07-07T04:59:23Z | |
| dc.date.available | 2026-07-07T04:59:23Z | |
| dc.description | Let Mod_{g,b} denote the mapping class group of a surface of genus g with b punctures. Feng Luo asked in a recent preprint if there is a universal upper bound, independent of genus, for the number of torsion elements needed to generate Mod_{g,b}. We answer Luo's question by proving that 3 torsion elements suffice to generate Mod_{g,0}. We also prove the more delicate result that there is an upper bound, independent of genus, not only for the number of torsion elements needed to generate Mod_{g,b} but also for the order of those elements. In particular, our main result is that 6 involutions (i.e. orientation-preserving diffeomorphisms of order two) suffice to generate Mod_{g,b} for every genus g >= 3, b = 0, and g >= 4, b = 1. | |
| dc.description | 15 pages, 7 figures; slightly improved main result; minor revisions. to appear in J. Alg | |
| dc.identifier | https://arxiv.org/abs/math/0307039 | |
| dc.identifier | http://arxiv.org/abs/math/0307039 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67961 | |
| dc.subject | Geometric Topology | |
| dc.subject | Group Theory | |
| dc.subject | 20F65 (Primary) 57M07, 20F38 (Secondary) | |
| dc.title | Every mapping class group is generated by 6 involutions | |
| dc.type | text |