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A Primer on Mapping Class Groups (PMS-49) by Dan Margalit, Benson Farb

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Chapter Twelve

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Moduli Space

The moduli space of Riemann surfaces is one of the fundamental objects of mathematics. It is ubiquitous, appearing as a basic object in fields from low-dimensional topology to algebraic geometry to mathematical physics. The moduli space m(S) parameterizes, among other things: isometry classes of hyperbolic structures on S, conformal classes of Riemannian metrics on S, biholomorphism classes of complex structures on S, and isomorphism classes of smooth algebraic curves homeomorphic to S.

We will access (S) as the quotient ...

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