Telescopic actions
  A group action H on X is called "telescopic" if for any finitely presented group G, there exists a subgroup H' in H such that G is isomorphic to the fundamental group of X/H'.   We construct examples of telescopic actions on some CAT[-1] spaces, in particular on 3 and 4-dimensional hyperbolic spaces. As applications we give new proofs of the following statements:   (1) Aitchison's theorem: Every finitely presented group G can appear as the fundamental group of M/J, where M is a compact 3-manifold and J is an involution which has only isolated fixed points;   (2) Taubes' theorem: Every finitely presented group G can appear as the fundamental group of a compact complex 3-manifold. 
D. Panov and A. Petrunin
math.GR math.DG