Tame Combings of Groups
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- by Michael L. Mihalik and Steven T. Tschantz PDF
- Trans. Amer. Math. Soc. 349 (1997), 4251-4264 Request permission
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.References
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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
- MR Author ID: 174820
- Email: tschantz@athena.cas.vanderbilt.edu
- Received by editor(s): July 11, 1995
- Received by editor(s) in revised form: March 22, 1996
- © Copyright 1997 American Mathematical Society
- 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