Realizing Countable Groups As Automorphism Groups of Riemann Surfaces

Every countable group can be realized as the full automorphism group of a Riemann surface as well as the full group of isometries of a Riemannian manifold.

2000 Mathematics Subject Classification: Primary 30F99, Secondary 20F29,20B27,32M05

Keywords and Phrases: Countable Groups, Full automorphism group, Riemann surface

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