Closed and transitive transformation groups of a surface

Abstract

The purpose of this paper is to survey the structure of closed and transitive transformation groups acting on a closed surface. In particular, we prove a number of relations between groups acting on the sphere that contain the rotation group, together with a diagram of how these groups are connected. In addition, we describe transformation groups acting on the torus and higher genus surfaces.

This preprint is the author's version of arXiv:1309.0179, with which it has substantial text overlap. That work was jointly authored with Fabio Tal, who no longer wishes to be included as an author