Abstract
A class of hyperbolic two-dimensional complexes X is defined. It is shown that the limit set of the action of π 1(X) on the universal covering \({\widetilde{X}}\) of X is equal to the visual boundary \({\partial \widetilde{X}}\) of and that \({\partial \widetilde{X}}\) is path connected and locally path connected. A kind of Sierpinski set is described which is homeomorphic to the visual boundary of certain ideal polyhedra.
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Emmanuel Vrontakis was supported by a graduate fellowship from the Greek Scholarship Foundation (I.K.Y.).
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Charitos, C., Papadoperakis, I. & Vrontakis, E. On the boundary of a special class of hyperbolic two-dimensional simplicial complexes. J. Geom. 94, 7–30 (2009). https://doi.org/10.1007/s00022-009-0002-x
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DOI: https://doi.org/10.1007/s00022-009-0002-x