Relative Free Splitting Complexes III: Stable Translation Lengths and Filling Paths
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910867662045184 |
|---|---|
| author | Handel, Michael Mosher, Lee |
| author_facet | Handel, Michael Mosher, Lee |
| contents | This is the last of a three part work about relative free splitting complexes $\mathcal{FS}(Γ,\mathscr{A})$ and their actions by relative outer automorphism groups $\text{Out}(Γ;\mathscr{A})$. We obtain quantitative relations between the stable translation length $τ_ϕ$ and the relative train track dynamics of~$ϕ\in \Out(Γ;\A)$. First, if $ϕ$ has an orbit with diameter bounded below by a certain constant $Ω(Γ;\mathscr{A}) \ge 1$ then $ϕ$ has a filling attracting lamination. Also, there is a positive lower bound $τ_ϕ\ge A(Γ;\mathscr{A}) > 0$ amongst all $ϕ$ which have a filling attracting lamination. Both proofs rely on a study of \emph{filling paths} in a free splitting. These results are all new even for $\text{Out}(F_n)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_07532 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Relative Free Splitting Complexes III: Stable Translation Lengths and Filling Paths Handel, Michael Mosher, Lee Group Theory 20F65 (primary) 57M07 (secondary) This is the last of a three part work about relative free splitting complexes $\mathcal{FS}(Γ,\mathscr{A})$ and their actions by relative outer automorphism groups $\text{Out}(Γ;\mathscr{A})$. We obtain quantitative relations between the stable translation length $τ_ϕ$ and the relative train track dynamics of~$ϕ\in \Out(Γ;\A)$. First, if $ϕ$ has an orbit with diameter bounded below by a certain constant $Ω(Γ;\mathscr{A}) \ge 1$ then $ϕ$ has a filling attracting lamination. Also, there is a positive lower bound $τ_ϕ\ge A(Γ;\mathscr{A}) > 0$ amongst all $ϕ$ which have a filling attracting lamination. Both proofs rely on a study of \emph{filling paths} in a free splitting. These results are all new even for $\text{Out}(F_n)$. |
| title | Relative Free Splitting Complexes III: Stable Translation Lengths and Filling Paths |
| topic | Group Theory 20F65 (primary) 57M07 (secondary) |
| url | https://arxiv.org/abs/2503.07532 |