2025/03/10 by Michael Handel, Lee Mosher, Handel, Michael +1
#math.GR
paper · pdf · doi:10.48550/arxiv.2503.07532
This is the last of a three part work about relative free splitting complexes FS(Γ,\mathscrA) and their actions by relative outer automorphism groups Out(Γ;\mathscrA). We obtain quantitative relations between the stable translation length τϕ and the relative train track dynamics of~ϕ∈ \Out(Γ;\A). First, if ϕ has an orbit with diameter bounded below by a certain constant Ω(Γ;\mathscrA) ≥ 1 then ϕ has a filling attracting lamination. Also, there is a positive lower bound τϕ≥ A(Γ;\mathscrA) > 0 amongst all ϕ which have a filling attracting lamination. Both proofs rely on a study of filling paths in a free splitting. These results are all new even for Out(Fn).