%0 Book Section
%T Tree-irreducible automorphisms of free groups
%+ Institut de Mathématiques de Marseille (I2M)
%A Lustig, Martin
%@ 978-3-319-05487-2
%B Extended Abstracts Fall 2012 (Automorphisms of Free Groups)
%I Springer International Publishing
%S Trends in Mathematics
%V 1
%P 67-71
%8 2014
%D 2014
%Z 1306.5688
%R 10.1007/978-3-319-05488-9_13
%K R-tree
%K indecomposable
%K iwip automorphism
%K outer space
%Z 20F; 20E, 57M
%Z Mathematics [math]/Group Theory [math.GR]Book sections
%X We introduce a new class of automorphisms $\varphi$ of the non-abelian free group $F_N$ of finite rank $N \geq 2$ which contains all iwips (= fully irreducible automorphisms), but also any automorphism induced by a pseudo-Anosov homeomorphism of a surface with arbitrary many boundary components. More generally, there may be subgroups of $F_N$ of rank $\geq 2$ on which $\varphi$ restricts to the identity. We prove some basic facts about such {\em tree-irreducible} automorphisms, and show that, together with Dehn twist automorphisms, they are the natural basic building blocks from which any automorphism of $\FN$ can be constructed in a train track set-up. We then show: {\bf Theorem:} {\it Every tree-irreducible automorphism of $F_N$ has induced North-South dynamics on the Thurston compactification $\bar{\rm CV}_N$ of Outer space.} Finally, we define a "blow-up" construction on the vertices of a train track map, which, starting from iwips, produces tree-irreducible automorphisms which in general are not iwip.
%G English
%L hal-01318467
%U https://hal.science/hal-01318467
%~ CNRS
%~ UNIV-AMU
%~ EC-MARSEILLE
%~ I2M
%~ I2M-2014-