A generalized weight test with applications to tree presentations
We introduce the ``cycle test'', which is a generalization of Gersten's ``weight test'', to study diagrammatic reducibility of standard 2- complexes. Diagrammatic reducibility (DR) is a stronger combinatorial form of asphericity for 2-complexes. A homogeneous version of the cycle test leads to conditions that generalize small cancellation theory in its application as a test for DR; a fact which also has been observed by Gersten. Aside from that, the cycle test has many applications in a nonhomogeneous way, of which we present several examples. In particular, some of these examples are related to ``labelled oriented tree'' presentations whose 2-complexes are spines of ribbon disk complements.
scientific article; zbMATH DE number 126404
scientific article