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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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 $1\to A\to G\to B\to 1$ 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

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02015-2
PII: S 0002-9947(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