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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Note on the Hurwitz-Nielsen realisation problem
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by C. Maclachlan PDF
Proc. Amer. Math. Soc. 64 (1977), 87-90 Request permission


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
  • © Copyright 1977 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 64 (1977), 87-90
  • MSC: Primary 55E99; Secondary 57E05, 32G15, 30A46
  • DOI:
  • MathSciNet review: 0442928