### Canonical Polygons for Finitely Generated Fuchsian Groups

New York University, 1964

Abstract

Fricke defined the concept of a canonical fundamental polygon for a finitely generated Fuchsian groups. His polygon is not canonical in the present technical sense of the word and his proof is complicated. In this thesis Fricke's definition is strengthened. The strengthened definition determines the polygon uniquely in terms of a standard system of generators of G. An independent proof of the existence of this new polygon is given. The proof uses quasiconformal mappings.