A. Petrunin

  1. Telescopic actions.

    Authors: D. Panov, A. Petrunin
    Subjects: Group Theory
    Abstract

    A group action $\Gamma$ on $X$ is called "telescopic" if for any finitely
    presented group $G$, there exists a subgroup $\Gamma'$ in $\Gamma$ such that
    $G$ is isomorphic to the fundamental group of $X/\Gamma'$.

    We construct some examples of telescopic actions. As an application we give
    an alternative proof of Taubes' theorem: "For every finitely presented group
    $G$ there exists a smooth compact complex 3-manifold with fundamental group
    isomorphic to $G$."

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