On minimal generating sets for the mapping class group of a punctured surface

Abstract

Let 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.