Abstract
AbstractLet Σg,p be an oriented surface of genus g with p punctures. We denote by $$\cal{M}_{g,p}$$
M
g
,
p
and $$\cal{M}_{g,p}^{\pm}$$
M
g
,
p
±
the mapping class group and the extended mapping class group of Σg,p, respectively. In this paper, we show that $$\cal{M}_{g,p}$$
M
g
,
p
and $$\cal{M}_{g,p}^{\pm}$$
M
g
,
p
±
are generated by two elements for g ≥ 3 and p ≥ 0.
Publisher
Springer Science and Business Media LLC
Reference33 articles.
1. T. Altunoz, M. Pamuk and O. Yildiz, Generating the extended mapping class group by three involutions, Osaka Journal of Mathematics 60 (2023), 61–75.
2. R. I. Baykur and M. Korkmaz, The mapping class group is generated by two commutators, Journal of Algebra 574 (2021), 278–291.
3. J. Birman, Mapping class groups and their relationship to braid groups, Communications in Pure and Applied Mathematics 22 (1969), 213–238.
4. T. E. Brendle and B. Farb, Every mapping class group is generated by 3 torsion elements and by 6 involutions, Journal of Algebra 278 (2004), 187–198.
5. M. Dehn, Die Gruppe der Abbildungsklassen, Acta Mathematica 69 (1938), 135–206.