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Transactions of the American Mathematical Society

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Geodesic currents and length compactness for automorphisms of free groups


Author: Stefano Francaviglia
Journal: Trans. Amer. Math. Soc. 361 (2009), 161-176
MSC (2000): Primary 20F65
DOI: https://doi.org/10.1090/S0002-9947-08-04420-6
Published electronically: August 13, 2008
MathSciNet review: 2439402
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Abstract: 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
Email: s.francaviglia@sns.it

DOI: https://doi.org/10.1090/S0002-9947-08-04420-6
Keywords: Automorphisms, free groups, geodesic currents
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.
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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