vix.ing · top · new · best · stats · spec

The boundary of the free splitting graph and the free factor graph

2012/11/07 by Ursula Hamenstaedt, Hamenstaedt, Ursula · 1 citation
Computer Science · Mathematics · #20F34 #20F65 #75M07 #Advanced Graph Theory Research #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #math.GT #msc:20F34 #msc:20F65 #msc:75M07

paper · pdf · doi:10.48550/arxiv.1211.1630

Argument clarified and streamlined. Details added. 60p

openalex publication_date 2012/11/07 · arxiv created 2014/08/25 · arxiv updated 2014/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the Gromov boundary of the free factor graph for the free group Fn with n>2 generators is the space of equivalence classes of minimal very small indecomposable projective Fn-trees without point stabilizer containing a free factor equipped with a quotient topology. Here two such trees are equivalent if the union of their metric completions with their Gromov boundaries are Fn-equivariantly homeomorphic with respect to the observer's topology. The boundary of the cyclic splitting graph is the space of equivalence classes of trees which either are indecomposable or split as very large graph of actions. The boundary of the free splitting graph is the space of equivalence classes of trees which either are indecomposable or split as large graph of actions.

Cited by

Related