Index realization for automorphisms of free groups
Résumé
For any surface Σ of genus g≥1 and (essentially) any collection of positive integers i1,i2,…,iℓ with i1+⋯+iℓ=4g−4 Masur and Smillie have shown that there exists a pseudo-Anosov homeomorphism h:Σ→Σ with precisely ℓ singularities S1,…,Sℓ in its stable foliation L, such that L has precisely ik+2 separatrices raying out from each Sk. In this paper we prove the analogue of this result for automorphisms of a free group FN, where "pseudo-Anosov homeomorphism" is replaced by "fully irreducible automorphism" and the Gauss-Bonnet equality i1+⋯+iℓ=4g−4 is replaced by the index inequality i1+⋯+iℓ≤2N−2 from Gaboriau, Jaeger, Levitt and Lustig.