Telescopic actions

D. Panov, A. Petrunin

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)1814-1831
Number of pages18
JournalGeometric and Functional Analysis
Volume22
Issue number6
DOIs
StatePublished - Dec 2012

All Science Journal Classification (ASJC) codes

  • Analysis
  • Geometry and Topology

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