Geodesic
Star-complexes, and the dependence problems for hyperbolic complexes
Glasgow mathematical journal, Tome 30 (1988) no. 2, pp. 155-170

Voir la notice de l'article provenant de la source Cambridge University Press

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: ⃗L (”strong mappings”) one gets an induced mapping φst: st⃗Lst 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). 
Pride, Stephen J. Star-complexes, and the dependence problems for hyperbolic complexes. Glasgow mathematical journal, Tome 30 (1988) no. 2, pp. 155-170. doi: 10.1017/S0017089500007175
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