Published online by Cambridge University Press: 24 October 2008
Spherical diagrams were introduced by Lyndon and Schupp[14] in order to study asphericity in group presentations and in 2-complexes. They have since been studied by several authors [2, 3, 5]. In particular, some technical loopholes in the original approach were closed in [5]. For many purposes the dual notion of pictures, introduced by Rourke[17], is more useful. These arise naturally through transversality. Pictures have also been studied and applied in [2, 5, 6, 12, 19].