Detection of fully irreducible automorphisms in generalized\n Baumslag-Solitar groups

2022/05/18 by Chloé Papin, Papin, Chloé
Mathematics · #20E08 #20F65 #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2205.08791

openalex publication_date 2022/05/18 · openalex created_date 2022/11/05 · openalex updated_date 2026/07/28

Abstract

We define fully irreducible automorphisms of generalized Baumslag-Solitar\ngroups in analogy with fully irreducible automorphisms of free groups. We first\nobtain a characterization of fully irreducible automorphisms analogous to a\ncondition given by Kapovich. Next we discuss the existence of pseudo-periodic\nconjugacy classes based on the study of Nielsen paths in a train track\nrepresentative. Finally we give an algorithm which finds out whether an\nautomorphism with a train track representative is pseudo-atoroidal and fully\nirreducible.\n

Related

• Tree-irreducible automorphisms of free groups
• Detecting fully irreducible automorphisms: a polynomial time algorithm. With an appendix by Mark C. Bell
• Whitehead algorithm for automorphisms of generalized Baumslag-Solitar groups
• An algorithm to detect full irreducibility by bounding the volume of periodic free factors
• On the isomorphism problem for generalized Baumslag-Solitar groups: invariants and flexible configurations