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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48.

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Measuring the tameness of almost convex groups
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by Susan Hermiller and John Meier PDF
Trans. Amer. Math. Soc. 353 (2001), 943-962 Request permission


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.
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Additional Information
  • Susan Hermiller
  • Affiliation: Department of Mathematics and Statistics, University of Nebraska, Lincoln, Nebraska 68588-0323
  • MR Author ID: 311019
  • Email:
  • John Meier
  • Affiliation: Department of Mathematics, Lafayette College, Easton, Pennsylvania 18042
  • Email:
  • 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:
  • MathSciNet review: 1804409