{"paper":{"title":"On property (T) for $\\operatorname{Aut}(F_n)$ and $\\operatorname{SL}_n(\\mathbb{Z})$","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.OA","authors_text":"Dawid Kielak, Marek Kaluba, Piotr W. Nowak","submitted_at":"2018-12-09T10:27:55Z","abstract_excerpt":"We prove that $\\operatorname{Aut}(F_n)$ has Kazhdan's property (T) for every $n \\geqslant 6$. Together with a previous result of Kaluba, Nowak, and Ozawa, this gives the same statement for $n\\geqslant 5$.\n  We also provide explicit lower bounds for the Kazhdan constants of $\\operatorname{SAut}(F_n)$ (with $n \\geqslant 6$) and of $\\operatorname{SL}_n(\\mathbb{Z})$ (with $n \\geqslant 3$) with respect to natural generating sets. In the latter case, these bounds improve upon previously known lower bounds whenever $n > 6$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.03456","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/1812.03456/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"}