Group extensions and tame pairs

Author:
Michael L. Mihalik

Journal:
Trans. Amer. Math. Soc. **351** (1999), 1095-1107

MSC (1991):
Primary 57N10, 57M10, 20F32

MathSciNet review:
1443200

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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 is an exact sequence of infinite finitely presented groups or if is an ascending HNN-extension with base and is a certain type of finitely presented subgroup of , then the pair 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

DOI:
http://dx.doi.org/10.1090/S0002-9947-99-02015-2

Received by editor(s):
August 5, 1996

Received by editor(s) in revised form:
January 22, 1997

Article copyright:
© Copyright 1999
American Mathematical Society