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Proceedings of the American Mathematical Society

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



Modulus space is simply-connected

Author: Colin Maclachlan
Journal: Proc. Amer. Math. Soc. 29 (1971), 85-86
MSC: Primary 30.45
MathSciNet review: 0286995
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Abstract: Modulus space of genus g consists of conformal equivalence classes of compact Riemann surfaces of genus g. It is the quotient space of the real Teichmuller space of marked Riemann surfaces by the Teichmuller modular group. The result follows using generators and some relations of this group and the fact that it acts discontinuously on Teichmuller space.

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Keywords: Compact Riemann surface, Fuchsian group, Teichmuller space, Teichmuller modular group, generators and relations
Article copyright: © Copyright 1971 American Mathematical Society