{"paper":{"title":"Constructing proper affine actions via higher strip deformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.GR"],"primary_cat":"math.GT","authors_text":"Ne\\v{z}a \\v{Z}ager Korenjak","submitted_at":"2022-05-29T16:39:34Z","abstract_excerpt":"We introduce higher strip deformations, which give a way of constructing affine deformations of discrete free groups in the image of the irreducible representation $\\operatorname{PSL}_2\\mathbb{R}\\to \\operatorname{SO}(2n,2n-1)$. We use the Margulis invariant to find a properness condition for these deformations, showing that each convex cocompact free group admits affine deformations acting properly on $\\mathbb{R}^{4n-1}$. Using our method we can also construct proper affine actions of virtually free groups, which we demonstrate by finding proper actions of $C_2 \\star C_3$ on $\\mathbb{R}^7.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.14712","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/2205.14712/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"}