{"paper":{"title":"Topological dynamical systems associated to II_1 factors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Nathanial P. Brown","submitted_at":"2010-10-06T17:35:55Z","abstract_excerpt":"If $N \\subset \\R$ is a separable II$_1$-factor, the space $\\Hom(N,\\R)$ of unitary equivalence classes of unital *-homomorphisms $N \\to \\R$ is shown to have a surprisingly rich structure. If $N$ is not hyperfinite, $\\Hom(N,\\R)$ is an infinite-dimensional, complete, metrizeable topological space with convex-like structure, and the outer automorphism group $\\Out(N)$ acts on it by \"affine\" homeomorphisms. (If $N \\cong R$, then $\\Hom(N,\\R)$ is just a point.) Property (T) is reflected in the extreme points -- they're discrete in this case. For certain free products $N = \\Sigma \\ast R$, every countab"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.1214","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"}