Classification of automorphism groups, up to topological equivalence, of compact Riemann surfaces of genus 4
type: Item
instance of: scholarly article
title: Classification of automorphism groups, up to topological equivalence, of compact Riemann surfaces of genus 4
zbMATH Open document ID: 1027.30063
DOI: 10.1016/S0021-8693(03)00138-8
author: Hideyuki Kimura
published in: Journal of Algebra
publication date: 2003-07-29T00:00:00Z
review text: Let \((X,G)\) be a pair of a compact Riemann surface of genus \(g>1\) and a group of automorphisms of \(X\). A pair \((X_1,G_1)\) is said to be topologically equivalent to \((X_2,G_2)\) if there exist an orientation preserving homeomorphism \(h:X_1 \to X_2\) and an isomorphism \(\iota :G_1 \to G_2\) such that \(\iota(\sigma)\circ h=h\circ \sigma\) for every \(\sigma \in G_1\). In the case \(g=4\), the author classifies \((X,G)\)'s up to topological equivalence and shows that there are 75 topological equivalence classes. In order to classify \((X,G)\)'s, the author considers surface kernel homomorphisms \(\varphi:\Gamma \to G\) and classifies them up to topological equivalence by using the works of \textit{I. Kuribayashi} and \textit{A. Kuribayashi} [J. Pure Appl. Algebra 65, No. 3, 277-292 (1990; Zbl 0709.30036)] on the matrix representation of Aut\((X)\) and branching data.
reviewed by: Gou Nakamura
Mathematics Subject Classification ID: 30F10
zbMATH DE Number: 1955946
zbMATH Keywords: compact Riemann surface
zbMATH Keywords: automorphism group
zbMATH Keywords: topological equivalence
MaRDI profile type: Publication
cites work: Q4502840
cites work: Classifying finite group actions on surfaces of low genus
cites work: CYCLIC GROUPS OF AUTOMORPHISMS OF A COMPACT RIEMANN SURFACE
cites work: Canonical polygons for finitely generated Fuchsian groups
cites work: Q4442375
cites work: Automorphism groups of compact Riemann surfaces of genera three and four
cites work: On automorphism groups of compact Riemann surfaces of genus 4
description: scientific article; zbMATH DE number 1955946