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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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.
References
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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