12 research outputs found
Telescopic actions
Get PDFA 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.Comment: +higher dimension
