On the boundary of a special class of hyperbolic two-dimensional simplicial complexes

摘要

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 [(X)tilde]{widetilde{X}} of X is equal to the visual boundary ¶[(X)tilde]{partial widetilde{X}} of and that ¶[(X)tilde]{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.