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Star-complexes, and the dependence problems for hyperbolic complexes

  • Stephen J. Pride (a1)
Abstract

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).

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12.S. J. Pride , On Tits' conjecture and other questions concerning Artin and generalized Artin groups, Invent. Math., 86 (1986), 347356.

14.M. Gromov , Hyperbolic groups in Essays in group theory, edited by S. M. Gersten (Springer-Verlag, 1987).

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Glasgow Mathematical Journal
  • ISSN: 0017-0895
  • EISSN: 1469-509X
  • URL: /core/journals/glasgow-mathematical-journal
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