Computing equivalence classes of finite group actions on orientable surfaces

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F24%3A43971338" target="_blank" >RIV/49777513:23520/24:43971338 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0022404923002608?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0022404923002608?via%3Dihub</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jpaa.2023.107578" target="_blank" >10.1016/j.jpaa.2023.107578</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Computing equivalence classes of finite group actions on orientable surfaces

Popis výsledku v původním jazyce

This paper focuses on the classification of classes of topological equivalence of finite group actions on Riemann surfaces. By the Riemann-Hurwitz bound, there are just finitely many groups that act conformally on a closed orientable surface Sg of genus g≥2. With each such action of a group G on Sg one can associate the fundamental group Γ=π(O) of the quotient orbifold O=Sg/G, isomorphic to a Fuchsian group determined completely by orbifold&apos;s signature. The Riemann existence theorem reduces the problem of the existence of an action of G on Sg to a purely group-theoretical problem of deciding whether there is an smooth epimorphism mapping the Fuchsian group Γ onto the group G. Using computer algebra systems such as MAGMA or GAP, together with the library of small groups, the generation of all finite group actions on a surface of fixed small genus g≥2 becomes almost a routine procedure. The difficult part is to determine the classes of these actions with respect to topological equivalence. To achieve this, one needs to investigate the action of the automorphism group of a Fuchsian group on the set of finite group actions on Sg with the corresponding signature. In this paper we derive several results on the topological equivalence of finite group actions on Riemann surfaces. As an application, we derive complete lists of finite group actions of genus g≤8 distinguished up to the topological equivalence.

Název v anglickém jazyce

Computing equivalence classes of finite group actions on orientable surfaces

Popis výsledku anglicky

This paper focuses on the classification of classes of topological equivalence of finite group actions on Riemann surfaces. By the Riemann-Hurwitz bound, there are just finitely many groups that act conformally on a closed orientable surface Sg of genus g≥2. With each such action of a group G on Sg one can associate the fundamental group Γ=π(O) of the quotient orbifold O=Sg/G, isomorphic to a Fuchsian group determined completely by orbifold&apos;s signature. The Riemann existence theorem reduces the problem of the existence of an action of G on Sg to a purely group-theoretical problem of deciding whether there is an smooth epimorphism mapping the Fuchsian group Γ onto the group G. Using computer algebra systems such as MAGMA or GAP, together with the library of small groups, the generation of all finite group actions on a surface of fixed small genus g≥2 becomes almost a routine procedure. The difficult part is to determine the classes of these actions with respect to topological equivalence. To achieve this, one needs to investigate the action of the automorphism group of a Fuchsian group on the set of finite group actions on Sg with the corresponding signature. In this paper we derive several results on the topological equivalence of finite group actions on Riemann surfaces. As an application, we derive complete lists of finite group actions of genus g≤8 distinguished up to the topological equivalence.

Druh

J_SC - Článek v periodiku v databázi SCOPUS

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

JOURNAL OF PURE AND APPLIED ALGEBRA

ISSN

0022-4049

e-ISSN

1873-1376

Svazek periodika

228

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

26

Strana od-do

—

Kód UT WoS článku

—

EID výsledku v databázi Scopus

2-s2.0-85179779607