## Measuring the tameness of almost convex groups

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- by Susan Hermiller and John Meier
- Trans. Amer. Math. Soc.
**353**(2001), 943-962 - DOI: https://doi.org/10.1090/S0002-9947-00-02717-3
- Published electronically: October 11, 2000
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## Abstract:

A 1-combing for a finitely presented group consists of a continuous family of paths based at the identity and ending at points $x$ in the 1-skeleton of the Cayley 2-complex associated to the presentation. We define two functions (radial and ball tameness functions) that measure how efficiently a 1-combing moves away from the identity. These functions are geometric in the sense that they are quasi-isometry invariants. We show that a group is almost convex if and only if the radial tameness function is bounded by the identity function; hence almost convex groups, as well as certain generalizations of almost convex groups, are contained in the quasi-isometry class of groups admitting linear radial tameness functions.## References

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## Bibliographic Information

**Susan Hermiller**- Affiliation: Department of Mathematics and Statistics, University of Nebraska, Lincoln, Nebraska 68588-0323
- MR Author ID: 311019
- Email: smh@math.unl.edu
**John Meier**- Affiliation: Department of Mathematics, Lafayette College, Easton, Pennsylvania 18042
- Email: meierj@lafayette.edu
- Received by editor(s): June 21, 1999
- Published electronically: October 11, 2000
- Additional Notes: Susan Hermiller acknowledges support from NSF grant DMS-9623088

John Meier acknowledges support from NSF RUI grant DMS-9704417 - © Copyright 2000 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**353**(2001), 943-962 - MSC (2000): Primary 20F65; Secondary 20F69, 57M07
- DOI: https://doi.org/10.1090/S0002-9947-00-02717-3
- MathSciNet review: 1804409