An algorithm for cellular maps of closed surfaces (Q1384139)

Some diagrammatic methods are described and used to reprove some topological results of Kneser, Edmonds and Skora. Considering several types of homomorphisms between surface groups, the authors gave an algorithm to apply certain homotopy equivalences to obtain normal-form maps. These maps are classified into three types. They could be branched coverings, pinchings or maps, collapsing graphs of punctured spheres to graphs immersed in the one-skeleton of the target surface. By means of this algorithm, one can give proofs of algebraic results on homomorphisms between surface groups.