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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The expansion factors of an outer automorphism and its inverse


Authors: Michael Handel and Lee Mosher
Journal: Trans. Amer. Math. Soc. 359 (2007), 3185-3208
MSC (2000): Primary 20E05; Secondary 20E36, 20F65
Published electronically: February 8, 2007
MathSciNet review: 2299451
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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
Email: michael.handel@lehman.cuny.edu

Lee Mosher
Affiliation: Department of Mathematics and Computer Science, Rutgers University at Newark, Newark, New Jersey 07102
Email: mosher@andromeda.rutgers.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-07-04066-4
PII: S 0002-9947(07)04066-4
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.
Article copyright: © Copyright 2007 American Mathematical Society