{"paper":{"title":"Relative free splitting and free factor complexes: An overview","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Lee Mosher, Michael Handel","submitted_at":"2026-07-21T16:19:06Z","abstract_excerpt":"For any group $\\Gamma$ and any free factor system~$\\mathscr A$ of $\\Gamma$, the relative outer automorphism group $\\text{Out}(\\Gamma;\\mathscr A)$ acts naturally on the relative free splitting complex $\\mathcal{F\\!S}(\\Gamma;\\mathscr A)$ and on the complex of relative free factor systems $\\mathcal{F\\!F}(\\Gamma;\\mathscr A)$, generalizing the well known actions of $\\text{Out}(F_n)$ on the absolute free splitting complex $\\mathcal{F\\!S}(F_n)$ and the absolute free factor complex ${\\mathcal{F}}(F_n)$ of the rank~$n$ free group~$F_n$.\n  This overview summarizes a three part work regarding the large s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.19249","kind":"arxiv","version":1},"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/2607.19249/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"}