Skip to Main Content

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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Combinatorics of tight geodesics and stable lengths
HTML articles powered by AMS MathViewer

by Richard C. H. Webb PDF
Trans. Amer. Math. Soc. 367 (2015), 7323-7342 Request permission


We give an algorithm to compute the stable lengths of pseudo-Anosovs on the curve graph, answering a question of Bowditch. We also give a procedure to compute all invariant tight geodesic axes of pseudo-Anosovs.

Along the way we show that there are constants $1<a_1<a_2$ such that the minimal upper bound on ‘slices’ of tight geodesics is bounded below and above by $a_1^{\xi (S)}$ and $a_2^{\xi (S)}$, where $\xi (S)$ is the complexity of the surface. As a consequence, we give the first computable bounds on the asymptotic dimension of curve graphs and mapping class groups.

Our techniques involve a generalization of Masur–Minsky’s tight geodesics and a new class of paths on which their tightening procedure works.

Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 57M99, 20F65
  • Retrieve articles in all journals with MSC (2010): 57M99, 20F65
Additional Information
  • Richard C. H. Webb
  • Affiliation: Mathematics Institute, University of Warwick, Coventry, CV4 7AL, United Kingdom
  • Address at time of publication: Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, United Kingdom
  • MR Author ID: 1104740
  • ORCID: 0000-0001-9161-0928
  • Email:,
  • Received by editor(s): May 27, 2013
  • Received by editor(s) in revised form: October 13, 2013
  • Published electronically: April 3, 2015
  • Additional Notes: This work was supported by the Engineering and Physical Sciences Research Council Doctoral Training Grant.
  • © Copyright 2015 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 367 (2015), 7323-7342
  • MSC (2010): Primary 57M99; Secondary 20F65
  • DOI:
  • MathSciNet review: 3378831