| In this dissertation, examples of flat surfaces with infinite genus and finite area are constructed. It is shown that the automorphism groups of these surfaces are non-elementary Fuchsian groups of the second kind. In certain cases the automorphism group is infinitely generated. This gives an explicit construction of Teichmüller disks in the Teichmüller space of a surface of infinite genus X, stabilized by large sub-groups of the mapping class group of X. |
