Flat 2-orbifolds and Seifert fibred 4-manifolds

Abstract

This is a summary of some of the basic facts about flat 2-orbifold groups, otherwise known as 2-dimensional crystallographic groups. We relate the geometric and topological presentations of these groups, and consider structures corresponding to decompositions of the orbifolds as fibrations or as unions. We also consider covering relations, and record the bases of Seifert fibrations of 4-manifolds with geometries of solvable Lie type.