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Tame Combings of Groups


Authors: Michael L. Mihalik and Steven T. Tschantz
Journal: Trans. Amer. Math. Soc. 349 (1997), 4251-4264
MSC (1991): Primary 20F05; Secondary 57M20
DOI: https://doi.org/10.1090/S0002-9947-97-01772-8
MathSciNet review: 1390045
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Abstract: In this paper, we introduce the idea of tame combings for finitely presented groups. If $M$ is a closed irreducible 3-manifold and $\pi _{1}(M)$ is tame combable, then the universal cover of $M$ is homeomorphic to ${\mathbb {R}}^{3}$. We show that all asynchronously automatic and all semihyperbolic groups are tame combable.


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Additional Information

Michael L. Mihalik
Affiliation: Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240
Email: mihalikm@ctrvax.vanderbilt.edu

Steven T. Tschantz
Affiliation: Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240
Email: tschantz@athena.cas.vanderbilt.edu

DOI: https://doi.org/10.1090/S0002-9947-97-01772-8
Received by editor(s): July 11, 1995
Received by editor(s) in revised form: March 22, 1996
Article copyright: © Copyright 1997 American Mathematical Society

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