Open Access
Winter 2015 Index realization for automorphisms of free groups
Thierry Coulbois, Martin Lustig
Illinois J. Math. 59(4): 1111-1128 (Winter 2015). DOI: 10.1215/ijm/1488186023

Abstract

For any surface $\Sigma$ of genus $g\geq1$ and (essentially) any collection of positive integers $i_{1},i_{2},\ldots,i_{\ell}$ with $i_{1}+\cdots+i_{\ell}=4g-4$ Masur and Smillie (Comment. Math. Helv. 68 (1993) 289–307) have shown that there exists a pseudo-Anosov homeomorphism $h:\Sigma\to\Sigma$ with precisely $\ell$ singularities $S_{1},\ldots,S_{\ell}$ in its stable foliation $\mathcal{L}$, such that $\mathcal{L}$ has precisely $i_{k}+2$ separatrices raying out from each $S_{k}$.

In this paper, we prove the analogue of this result for automorphisms of a free group ${F}_{N}$, where “pseudo-Anosov homeomorphism” is replaced by “fully irreducible automorphism” and the Gauss–Bonnet equality $i_{1}+\cdots+i_{\ell}=4g-4$ is replaced by the index inequality $i_{1}+\cdots+i_{\ell}\leq2N-2$ from (Duke Math. J. 93 (1998) 425–452).

Citation

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Thierry Coulbois. Martin Lustig. "Index realization for automorphisms of free groups." Illinois J. Math. 59 (4) 1111 - 1128, Winter 2015. https://doi.org/10.1215/ijm/1488186023

Information

Received: 2 May 2016; Revised: 5 December 2016; Published: Winter 2015
First available in Project Euclid: 27 February 2017

zbMATH: 1382.20030
MathSciNet: MR3628303
Digital Object Identifier: 10.1215/ijm/1488186023

Subjects:
Primary: 20E05 , 20E08 , 20F65 , 57R30

Rights: Copyright © 2015 University of Illinois at Urbana-Champaign

Vol.59 • No. 4 • Winter 2015
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