Boundary of the Relative Outer Space

Abstract

Let $\mathcal{A}=A_1,...,A_k$ be a system of free factors of $F_n$. The group of relative automorphisms $\mathrm{Aut}(F_n;\mathcal{A})$ is the group given by the automorphisms of $F_n$ that restricted to each $A_i$ are conjugations by elements in $F_n$. The group of relative outer automorphisms is defined as $\mathrm{Out}(F_n;\mathcal{A})=\mathrm{Aut}(F_n;\mathcal{A})/\mathrm{Inn}(F_n)$, where $\mathrm{Inn (F_n)$ is the normal subgroup of $\mathrm{Aut}(F_n)$ given by all the inner automorphisms. This group acts on the relative outer space ${\mathrm{CV}}_n(\mathcal{A})$. We prove that the dimension of the boundary of the relative outer space is $\dim ({\mathrm{CV}}_n(\mathcal{A}))-1$.

13 pages, 1 figure

References in corpus (2)

• Deformation and rigidity of simplicial group actions on trees
• Relative outer automorphisms of free groups