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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality 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 1.43.

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The expansion factors of an outer automorphism and its inverse
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by Michael Handel and Lee Mosher PDF
Trans. Amer. Math. Soc. 359 (2007), 3185-3208 Request permission

Abstract:

A fully irreducible outer automorphism $\phi$ of the free group $F_n$ of rank $n$ has an expansion factor which often differs from the expansion factor of $\phi ^{-1}$. Nevertheless, we prove that the ratio between the logarithms of the expansion factors of $\phi$ and $\phi ^{-1}$ is bounded above by a constant depending only on the rank $n$. We also prove a more general theorem applying to an arbitrary outer automorphism of $F_n$ and its inverse and their two spectrums of expansion factors.
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Additional Information
  • Michael Handel
  • Affiliation: Department of Mathematics and Computer Science, Lehman College - CUNY, 250 Bedford Park Boulevard W, Bronx, New York 10468
  • MR Author ID: 223960
  • Email: michael.handel@lehman.cuny.edu
  • Lee Mosher
  • Affiliation: Department of Mathematics and Computer Science, Rutgers University at Newark, Newark, New Jersey 07102
  • MR Author ID: 248017
  • Email: mosher@andromeda.rutgers.edu
  • Received by editor(s): December 9, 2004
  • Received by editor(s) in revised form: April 22, 2005
  • Published electronically: February 8, 2007
  • Additional Notes: The first author was supported in part by NSF grant DMS0103435.
    The second author was supported in part by NSF grant DMS0103208.
  • © Copyright 2007 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 359 (2007), 3185-3208
  • MSC (2000): Primary 20E05; Secondary 20E36, 20F65
  • DOI: https://doi.org/10.1090/S0002-9947-07-04066-4
  • MathSciNet review: 2299451