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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Note on the Hurwitz-Nielsen realisation problem


Author: C. Maclachlan
Journal: Proc. Amer. Math. Soc. 64 (1977), 87-90
MSC: Primary 55E99; Secondary 57E05, 32G15, 30A46
MathSciNet review: 0442928
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Abstract: This problem, which is equivalent to the problem of showing that every finite subgroup of the Teichmüller modular group of a compact surface of genus g has a fixed point in the corresponding Teichmüller space, is solved for $ g = 2$. The generalised problem for n-punctured surfaces of genus $ g \geqslant 1$ and $ 1 \leqslant n \leqslant 4$ is also solved.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0442928-X
PII: S 0002-9939(1977)0442928-X
Keywords: Teichmüller space, Teichmüller modular group, Fuchsian group
Article copyright: © Copyright 1977 American Mathematical Society