Group extensions and tame pairs

Mihalik, Michael

doi:10.1090/S0002-9947-99-02015-2

Group extensions and tame pairs
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by Michael L. Mihalik PDF

Trans. Amer. Math. Soc. 351 (1999), 1095-1107 Request permission

Abstract:

Tame pairs of groups were introduced to study the missing boundary problem for covers of compact 3-manifolds. In this paper we prove that if $1\to A\to G\to B\to 1$ is an exact sequence of infinite finitely presented groups or if $G$ is an ascending HNN-extension with base $A$ and $H$ is a certain type of finitely presented subgroup of $A$, then the pair $(G,H)$ is tame. Also we develop a technique for showing certain groups cannot be the fundamental group of a compact 3-manifold. In particular, we give an elementary proof of the result of R. Bieri, W. Neumann and R. Strebel: A strictly ascending HNN-extension cannot be the fundamental group of a compact 3-manifold.

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