Growth and displacement of free product automorphisms

2023/07/25 by Collins, Matthew
#20E08 (Secondary) #20F65 (Primary) 20E36 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2307.13502

Abstract

It is well known for an irreducible free group automorphism that its growth rate is equal to the minimal Lipschitz displacement of its action on Culler-Vogtmann space. This follows as a consequence of the existence of train track representatives for the automorphism. We extend this result to the general - possibly reducible - case as well as to the free product situation where growth is replaced by `relative growth'.

Related

• Displacements of automorphisms of free groups I: Displacement functions,\n minpoints and train tracks
• Displacements of automorphisms of free groups II: Connectivity of level sets and decision problems
• On the connectivity of level sets of automorphisms of free groups, with applications to decision problems
• On the action of relatively irreducible automorphisms on their train tracks
• Fixed points of irreducible, displacement one automorphisms of free products