Classifying finite group actions on surfaces of low genus
type: Item
instance of: scholarly article
title: Classifying finite group actions on surfaces of low genus
zbMATH Open document ID: 0722.57005
DOI: 10.1016/0022-4049(91)90021-S
author: S. Allen Broughton
published in: Journal of Pure and Applied Algebra
publication date: 1990-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 57M60
zbMATH DE Number: 4190721
zbMATH Keywords: actions
zbMATH Keywords: finite groups
zbMATH Keywords: Fuchsian groups
zbMATH Keywords: fundamental groups
zbMATH Keywords: Riemann-Hurwitz formula
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4190721