{"paper":{"title":"The rigidity of some finite group actions on CAT($\\kappa$) spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Khek Lun Harold Chao","submitted_at":"2013-03-07T20:26:52Z","abstract_excerpt":"In this paper, we first prove the optimal lower bound for Alexandrov angle rigidity of torsion elliptic isometries on any complete CAT($\\kappa$) space, which, when attained, leads to an embedded 2-flat in the tangent cone invariant under the induced action of the isometry. Next, we will prove similar result for action of symmetry groups of either a regular orthoplex, a regular hypercube, a regular dodecahedron or a regular icosahedron on a set of points in any complete CAT($\\kappa$) space in a way corresponds to the set of vertices of the polytope, the angle made at the circumcenter by any pai"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.1801","kind":"arxiv","version":3},"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"}