## 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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## Additional Information

**Michael L. Mihalik**- Affiliation: Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240
- Email: mihalikm@ctrvax.vanderbilt.edu
- Received by editor(s): August 5, 1996
- Received by editor(s) in revised form: January 22, 1997
- © Copyright 1999 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**351**(1999), 1095-1107 - MSC (1991): Primary 57N10, 57M10, 20F32
- DOI: https://doi.org/10.1090/S0002-9947-99-02015-2
- MathSciNet review: 1443200