2013/06/24 by Martin Lustig, Lustig, Martin
Mathematics · #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR)
paper · doi:10.48550/arxiv.1306.5688
openalex publication_date 2013/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a new class of automorphisms φ of the non-abelian free group FN of finite rank N ≥ 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 FN of rank ≥ 2 on which φ 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 FN has induced North-South dynamics on the Thurston compactification \rm CVN 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.