Finiteness of polyhedral decompositions of cusped hyperbolic manifolds obtained by the Epstein-Penner's method (Q2719019)

This paper deals with noncompact complete orientable hyperbolic manifolds of finite volume. According to work by \textit{D. Epstein} and \textit{R. Penner} in J. Diff. Geom. 27, 67-80 (1988; Zbl 0611.53036) such a manifold admits a canonical decomposition into hyperbolic ideal polyhedra. This decomposition depends on arbitrarily specified weights for the cusps. The main result of the present paper states that for a given manifold the number of possible decompositions of this type is finite. The proof depends on specific results on the finiteness of so-called horoball patterns.