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Factoring periodic maps into Dehn twists

We give a classification up to conjugacy for irreducible periodic diffeomorphisms of a surface $\Sigma_{g}$ which commute with involutions $\iota$ such that $\Sigma_{g}/\langle \iota \rangle \cong T^{2}$. More generally, we classify finite subgroups of centralizers of irreducible periodic diffeomorphism.

On certain irreducible finite group actions on surfaces

We classify up to conjugacy the group generated by a commuting pair of a periodic diffeomorphism and a hyperelliptic involution on an oriented closed surface. This result can be viewed as a refinement of Ishizaka's result on classification of the mapping classes of hyperelliptic periodic diffeomorphisms. As an application, we obtain the Dehn twist presentations of hyperelliptic periodic mapping classes, which are closely related to the ones obtained by Ishizaka.

Norihisa Takahashi

Papers

Dehn twist presentations of hyperelliptic periodic diffeomorphisms on closed surfaces

Dehn twist presentations of hyperelliptic periodic diffeomorphisms on closed surfaces

On certain irreducible finite group actions on surfaces