Parageometric outer automorphisms of free groups
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- by Michael Handel and Lee Mosher PDF
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Abstract:
We study those fully irreducible outer automorphisms $\phi$ of a finite rank free group $F_r$ which are parageometric, meaning that the attracting fixed point of $\phi$ in the boundary of outer space is a geometric $\mathbf {R}$-tree with respect to the action of $F_r$, but $\phi$ itself is not a geometric outer automorphism in that it is not represented by a homeomorphism of a surface. Our main result shows that the expansion factor of $\phi$ is strictly larger than the expansion factor of $\phi ^{-1}$. As corollaries (proved independently by Guirardel), the inverse of a parageometric outer automorphism is neither geometric nor parageometric, and a fully irreducible outer automorphism $\phi$ is geometric if and only if its attracting and repelling fixed points in the boundary of outer space are geometric $\mathbf {R}$-trees.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), 3153-3183
- MSC (2000): Primary 20E05; Secondary 20E36, 20F65
- DOI: https://doi.org/10.1090/S0002-9947-07-04065-2
- MathSciNet review: 2299450