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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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Geodesic currents and length compactness for automorphisms of free groups
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by Stefano Francaviglia PDF
Trans. Amer. Math. Soc. 361 (2009), 161-176 Request permission


We prove a compactness theorem for automorphisms of free groups. Namely, we show that the set of automorphisms keeping the length of the uniform current bounded is compact (up to conjugation). This implies that the spectrum of the length of the images of the uniform current is discrete, proving a conjecture of I. Kapovich.
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Additional Information
  • Stefano Francaviglia
  • Affiliation: Departament de Matemàtiques, Edifici C, Universitat Autònoma, 08193 Bellaterra (Barcelona) Spain
  • MR Author ID: 677681
  • Email:
  • Received by editor(s): May 22, 2006
  • Received by editor(s) in revised form: October 25, 2006
  • Published electronically: August 13, 2008
  • Additional Notes: The author was supported by a Marie Curie Intra European Fellowship.
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 361 (2009), 161-176
  • MSC (2000): Primary 20F65
  • DOI:
  • MathSciNet review: 2439402