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\(\mathrm{Out}(F_3)\) index realization. (English) Zbl 1377.20021
Summary: By proving precisely which singularity index lists arise from the pair of invariant foliations for a pseudo-Anosov surface homeomorphism, H. Masur and J. Smillie [Comment. Math. Helv. 68, No. 2, 289–307 (1993; Zbl 0792.30030)] determined a Teichmüller flow invariant stratification of the space of quadratic differentials. In this paper we determine an analog to the theorem for \(\mathrm{Out}(F_3)\). That is, we determine which index lists permitted by the [D. Gaboriau et al., Duke Math. J. 93, No. 3, 425–452 (1998; Zbl 0946.20010)] index sum inequality are achieved by a geometric fully irreducible outer automorphisms of the rank-3 free group.

MSC:
20E36 Automorphisms of infinite groups
20E05 Free nonabelian groups
20F28 Automorphism groups of groups
20F65 Geometric group theory
30F60 Teichmüller theory for Riemann surfaces
32G15 Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables)
37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
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