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Star-complexes, and the dependence problems for hyperbolic complexes

Published online by Cambridge University Press:  18 May 2009

Stephen J. Pride
Stephen J. Pride
Affiliation:
Department of Mathematics, University of Glasgow, University Gardens, Glasgow G12 8QW
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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).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 30 , Issue 2 , May 1988 , pp. 155 - 170
Copyright
Copyright © Glasgow Mathematical Journal Trust 1988

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