Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the action of relatively irreducible automorphisms on their train
  tracks   Let $G$ be a group and let ${\mathcal G}$ be a free factor system of $G$,
namely a free splitting of $G$ as $G=G_1*\dots*G_k*F_r$. In this paper, we
study the set of train track points for ${\mathcal G}$-irreducible
automorphisms $\phi$ with exponential growth (relatively to ${\mathcal G}$).
Such set is known to coincide with the minimally displaced set
$\operatorname{Min}(\phi)$ of $\phi$.
  Our main result is that $\operatorname{Min}(\phi)$ is co-compact, under the
action of the cyclic subgroup generated by $\phi$.
  Along the way we obtain other results that could be of independent interest.
For instance, we prove that any point of $\operatorname{Min}(\phi)$ is in
uniform distance from $\operatorname{Min}(\phi^{-1})$. We also prove that the
action of $G$ on the product of the attracting and the repelling trees for
$\phi$, is discrete. Finally, we get some fine insight about the local topology
of relative outer space.
  As an application, we generalise a classical result of Bestvina, Feighn and
Handel for the centralisers of irreducible automorphisms of free groups, in the
more general context of relatively irreducible automorphisms of a free product.
We also deduce that centralisers of elements of $\operatorname{Out}(F_3)$ are
finitely generated, which was previously unknown. Finally, we mention that an
immediate corollary of co-compactness is that $\operatorname{Min}(\phi)$ is
quasi-isometric to a line.

22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph