Glasgow Mathematical Journal

Research Article

Star-complexes, and the dependence problems for hyperbolic complexes

Stephen J. Pridea1

a1 Department of Mathematics, University of Glasgow, University Gardens, Glasgow G12 8QW

Given a group presentation (or more generally† a 2-complex) one can associate with it an object which has variously been called the co-initial graph, star-graph, star-complex, and which has proved useful in several contexts [2], [6], [7], [8], [9], [10], [12]. For certain mappings of 2-complexes φ: S0017089500007175_inline1xs2112 (”strong mappings”) one gets an induced mapping φst: S0017089500007175_inline1stxs2112st of the associated star-complexes. Then st is a covariant functor from the category of 2-complexes (where the morphisms are strong mappings) to the category of 1-complexes, and this functor behaves very nicely with respect to coverings (Theorem 1).

(Received July 15 1986)