{"paper":{"title":"Invariant means for the wobbling group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.PR"],"primary_cat":"math.GR","authors_text":"Kate Juschenko, Mikael de la Salle","submitted_at":"2013-01-21T02:50:57Z","abstract_excerpt":"Given a metric space $(X,d)$, the wobbling group of $X$ is the group of bijections $g:X\\rightarrow X$ satisfying $\\sup\\limits_{x\\in X} d(g(x),x)<\\infty$. We study algebraic and analytic properties of $W(X)$ in relation with the metric space structure of $X$, such as amenability of the action of the lamplighter group $ \\bigoplus_{X} \\mathbf Z/2\\mathbf Z \\rtimes W(X)$ on $\\bigoplus_{X} \\mathbf Z/2\\mathbf Z$ and property (T)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4736","kind":"arxiv","version":4},"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"}