On a classification of irreducible periodic diffeomorphisms on surfaces which commute with certain involution

Abstract

Ishizaka classified up to conjugacy hyperelliptic periodic automorphisms of a surface. Here, an involution $I$ on a surface ${\Sigma }_g$ is hyperelliptic if and only if ${\Sigma }_g/⟨I⟩$ is homeomorphic to $S^2$. In this article, we give a classification up to conjugacy for irreducible periodic automorphisms of a surface ${\Sigma }_g$ which commute with involutions $\iota$ such that ${\Sigma }_g/⟨\iota ⟩$ is homeomorphic to $T^2$.

16 pages, 17 Figures