Revista Matemática Iberoamericana

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Volume 13, Issue 3, 1997, pp. 543–566
DOI: 10.4171/RMI/230

Published online: 1997-12-31

Some generalized Coxeter groups and their orbifolds

Marcel Hagelberg[1] and Rubén A. Hidalgo[2]

(1) Université Paul Sabatier, Toulouse, France
(2) Universidad Técnica Federico Santa María, Valparaíso, Chile

In this note we construct examples of geometric 3-orbifolds with (orbifold) fundamental group isomorphic to a ($\mathbb Z$-extension of a) generalized Coxeter group. Some of these orbifolds have either euclidean spherical or hyperbolic structure. As an application we obtain an alternative proof of theorem 1 of Hagelberg, Maclaughlan and Rosenberg in [5]. We also obtain a similar result for generalized Coxeter groups.

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Hagelberg Marcel, Hidalgo Rubén: Some generalized Coxeter groups and their orbifolds. Rev. Mat. Iberoam. 13 (1997), 543-566. doi: 10.4171/RMI/230