Telescopic actions

TY - JOUR

T1 - Telescopic actions

AU - Panov, D.

AU - Petrunin, A.

N1 - +higher dimensions

PY - 2012/12

Y1 - 2012/12

N2 - 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.

AB - 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.

U2 - 10.1007/s00039-012-0194-3

DO - 10.1007/s00039-012-0194-3

M3 - Article

SN - 1016-443X

VL - 22

SP - 1814

EP - 1831

JO - GEOMETRIC AND FUNCTIONAL ANALYSIS

JF - GEOMETRIC AND FUNCTIONAL ANALYSIS

IS - 6

ER -