The boundary of the complex of free factors

TL;DR

This paper characterizes the boundary of the free factor complex using geometric and structural tools, drawing parallels to the curve complex boundary in Teichmüller theory.

Contribution

It provides a novel description of the free factor complex boundary, extending techniques from folding paths and small tree structures.

Findings

Boundary description analogous to curve complex

Utilizes folding path geometry and small trees

Advances understanding of free factor complex structure

Abstract

We give a description of the boundary of a complex of free factors that is analogous to E. Klarreich's description of the boundary of a curve complex. The argument uses the geometry of folding paths developed by Bestvina and Feighn as well as structural results about very small trees developed by Coulbois, Hilion, Lustig, and Reynolds.