Mapping tori of small dilatation irreducible train-track maps

2012/09/25 by Yael Algom-Kfir, Algom-Kfir, Yael, Kasra Rafi +1
Computer Science · Mathematics · Medicine · #20E36 #57Mxx #Advanced Combinatorial Mathematics #Combinatorics #Computer science #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry #Integer (computer science) #Irreducible representation #Mathematical analysis #Mathematics #Medicine #Presentation (obstetrics) #Pure mathematics #Torus #Track (disk drive) #Upper and lower bounds #math.GT #msc:20E36 #msc:57Mxx #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1209.5635

Some figures in color

openalex publication_date 2012/09/25 · arxiv created 2012/11/23 · arxiv updated 2012/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

We prove that for every P there is a bound B depending only on P so that the mapping torus of every P--small irreducible train-track map can be obtained by surgery from one of B mapping tori. We show that given an integer P>0 there is a bound M depending only on P, so that there exists a presentation of the fundamental group of the mapping torus of a P--small irreducible train-track map with less than M generators and M relations.

Citations

• Hyperbolic automorphisms of free groups
• Laminations, trees, and irreducible automorphisms of free groups
• Cut points and canonical splittings of hyperbolic groups
• A family of pseudo-Anosov braids with small dilatation
• Train Tracks and Automorphisms of Free Groups
• Die Isomorphismengruppe der freien Gruppen

Related

• Small dilatation pseudo-Anosov mapping classes and short circuits on train track automata
• Irreducible train tracks for pseudo-Anosov homeomorphisms
• A lower bound on volumes of end-periodic mapping tori
• Essential minimum and obstruction degrees of translates of subtori
• Train track maps for graphs of groups