On the Involution Generators of the Mapping Class Group of a Punctured Surface

Let Mod(Σg,p)$$\textrm{Mod}(\Sigma _{g,p})$$ denote the mapping class group of a connected orientable surface of genus g with p punctures. For g≥14$$g\ge 14$$ and even p≥10$$p\ge 10$$, we prove that Mod(Σg,p)$$\textrm{Mod}(\Sigma _{g,p})$$ can be generated by three involutions. For g≥13$$g\ge 13$$ and even p≥9$$p\ge 9$$, we prove that Mod(Σg,p)$$\textrm{Mod}(\Sigma _{g,p})$$ can be generated by four involutions. Moreover, for even p≥4$$p\ge 4$$ …