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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On extendability of group actions on compact Riemann surfaces


Authors: Emilio Bujalance, F. J. Cirre and Marston Conder
Journal: Trans. Amer. Math. Soc. 355 (2003), 1537-1557
MSC (2000): Primary 20H10; Secondary 14H55, 20F38, 30F10
Published electronically: December 4, 2002
MathSciNet review: 1946404
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Abstract: The question of whether a given group $G$ which acts faithfully on a compact Riemann surface $X$ of genus $g\ge 2$ is the full group of automorphisms of $X$ (or some other such surface of the same genus) is considered. Conditions are derived for the extendability of the action of the group $G$ in terms of a concrete partial presentation for $G$associated with the relevant branching data, using Singerman's list of signatures of Fuchsian groups that are not finitely maximal. By way of illustration, the results are applied to the special case where $G$ is a non-cyclic abelian group.


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Additional Information

Emilio Bujalance
Affiliation: Departamento de Matemáticas Fundamentales, Facultad de Ciencias, UNED, c/ Senda del Rey s/n, 28040 Madrid, Spain
Email: eb@mat.uned.es

F. J. Cirre
Affiliation: Departamento de Matemáticas Fundamentales, Facultad de Ciencias, UNED, c/ Senda del Rey s/n, 28040 Madrid, Spain
Email: jcirre@mat.uned.es

Marston Conder
Affiliation: Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand
Email: conder@math.auckland.ac.nz

DOI: http://dx.doi.org/10.1090/S0002-9947-02-03184-7
PII: S 0002-9947(02)03184-7
Keywords: Riemann surface, automorphism group
Received by editor(s): December 10, 2001
Published electronically: December 4, 2002
Additional Notes: The first author was partially supported by DGICYT PB98-0017
The second author was partially supported by DGICYT PB98-0756
The third author was partially supported by N.Z. Marsden Fund UOA-810
Article copyright: © Copyright 2002 American Mathematical Society