Classifying finite group actions on surfaces of low genus
The actions of finite groups (of orientation preserving mappings) on closed orientable surfaces of genus 2 and 3 are classified up to topological equivalence. This corresponds to Fuchsian groups with subgroups isomorphic to the fundamental groups of these surfaces. Using the Riemann-Hurwitz formula the signatures of possible Fuchsian groups are strongly restricted. Partial results have been known, namely for cyclic and abelian groups or for the cases when the lift of the action to the universal covering is a \((2,3,7)\) triangle group. Some more actions are constructed in the article. By a case-by-case consideration the completeness of the list is obtained.
scientific article; zbMATH DE number 4190721
scientific article