## Realizing countable groups as automorphism groups of Riemann surfaces

### Summary

Summary: 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.

### Mathematics Subject Classification

30F99, 20F29, 20B27, 32M05

### Keywords/Phrases

countable groups, full automorphism group, Riemann surface