Modulus space is simply-connected

Maclachlan, Colin

doi:10.1090/S0002-9939-1971-0286995-X

Modulus space is simply-connected
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by Colin Maclachlan PDF

Proc. Amer. Math. Soc. 29 (1971), 85-86 Request permission

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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