{"paper":{"title":"Relative Free Splitting Complexes II: Stable Translation Lengths and the Two Over All Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Lee Mosher, Michael Handel","submitted_at":"2022-12-19T23:13:32Z","abstract_excerpt":"This is the second of a three part study of relative free splitting complexes $\\mathcal{FS}(\\Gamma;\\mathscr A)$, known from Part~I to be Gromov hyperbolic. Here and in~Part III we focus on stable translation lengths $\\tau_\\phi \\ge 0$ of the simplicial isometries of $\\mathcal{FS}(\\Gamma;\\mathscr A)$ induced by relative outer automorphisms $\\phi \\in \\text{Out}(\\Gamma;\\mathscr A)$, stating and proving quantitative generalizations of earlier theorems for $\\text{Out}(F_n)$. The main technical result proved here in Part~II is the \\emph{Two Over All Theorem}, which expresses a uniform exponential fla"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.09907","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2212.09907/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}