The boundary of the complex of free factors

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.

34 pages. minor updates for submission

References in corpus (3)

• On hyperbolicity of free splitting and free factor complexes
• Reducing systems for very small trees
• Dynamics of Irreducible Endomorphisms of $F_n$

Cited by in corpus (25)

• The co-surface graph and the geometry of hyperbolic free group extensions
• The boundary of the free splitting graph and the free factor graph
• Algebraic laminations for free products and arational trees
• The Poisson boundary of $\text{Out}(F_N)$
• Hyperbolic graphs for free products, and the Gromov boundary of the graph of cyclic splittings
• Central limit theorems for mapping class groups and $\text{Out}(F_N)$
• Boundaries of relative factor graphs and subgroup classification for automorphisms of free products
• North-South dynamics of hyperbolic free group automorphisms on the space of currents
• Algebraic Ending Laminations and Quasiconvexity
• Ergodic decompositions for folding and unfolding paths in Outer space
• A short proof of Handel and Mosher's alternative for subgroups of $\text{Out}(F_N)$
• Automorphisms of graphs of cyclic splittings of free groups
• Spectral theorems for random walks on mapping class groups and $\text{Out}(F_N)$
• Unicorn paths and hyperfiniteness for the mapping class group
• Trees, dendrites, and the Cannon-Thurston map
• Random trees in the boundary of Outer space
• Conical limit points and the Cannon-Thurston map
• Constructing non-uniquely ergodic arational trees
• Measure equivalence rigidity of $\mathrm{Out}(F_N)$
• Commensurations of subgroups of $\mathrm{Out}(F_N)$
• On the topological dimension of the Gromov boundaries of some hyperbolic $Out(F_N)$-graphs
• Cocycle superrigidity from higher rank lattices to $\mathrm{Out}(F_N)$
• The minimally displaced set of an irreducible automorphism is locally finite
• Limit sets of unfolding paths in Outer space
• Generic-case complexity of Whitehead's algorithm, revisited