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Random outer automorphisms of free groups: Attracting trees and their singularity structures
Ilya Kapovich, Joseph Maher, Catherine Pfaff +1
We prove that a "random" free group outer automorphism is an ageometric fully irreducible outer automorphism whose ideal Whitehead graph is a union of triangles. In particular, we…
Stable Strata of Geodesics in Outer Space
Yael Algom-Kfir, Ilya Kapovich, Catherine Pfaff
In this paper we propose an Outer space analogue for the principal stratum of the unit tangent bundle to the Teichmüller space of a closed hyperbolic surface .…
Normalizers and centralizers of cyclic subgroups generated by lone axis fully irreducible outer automorphisms
Yael Algom-Kfir, Catherine Pfaff
We let be an ageometric fully irreducible outer automorphism so that its Handel-Mosher axis bundle consists of a single unique axis. We show that the centralizer $Cen(\langleφ\…
Ideal Whitehead Graphs in Out(F_r) I: Some Unachieved Graphs
Catherine Pfaff
H. Masur and J. Smillie proved precisely which singularity index lists arise from pseudo-Anosov mapping classes. In search of an analogous theorem for outer automorphisms of free g…