## 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.## References

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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