{"paper":{"title":"Representations of groups with CAT(0) fixed point property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Olga Varghese","submitted_at":"2018-03-27T16:43:28Z","abstract_excerpt":"We show that certain representations over fields with positive characteristic of groups having CAT(0) fixed point property ${\\rm F}\\mathcal{B}_{\\widetilde{A}_n}$ have finite image. In particular, we obtain rigidity results for representations of the following groups: the special linear group over $\\mathbb{Z}$, $SL_k(\\mathbb{Z})$, the special automorphism group of a free group, ${\\rm SAut}(F_k)$, the mapping class group of a closed orientable surface, ${\\rm Mod}(\\Sigma_g)$, and many other groups.\n  In the case of characteristic zero we show that low dimensional complex representations of groups"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.10175","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":""},"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"}