{"paper":{"title":"On fundamental groups of tensor product $\\rm II_1$ factors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Yusuke Isono","submitted_at":"2016-08-23T09:14:53Z","abstract_excerpt":"Let $M$ be a $\\rm II_1$ factor and let $\\mathcal{F}(M)$ denote the fundamental group of $M$. In this article, we study the following property of $M$: for arbitrary $\\rm II_1$ factor $B$, we have $\\mathcal{F}(M \\overline{\\otimes} B)=\\mathcal{F}(M)\\mathcal{F}(B)$. We prove that for any subgroup $G\\leq \\mathbb{R}^*_+$ which is realized as a fundamental group of a $\\rm II_1$ factor, there exists a $\\rm II_1$ factor $M$ which satisfies this property and whose fundamental group is $G$. Using this, we deduce that if $G,H \\leq \\mathbb{R}^*_+$ are realized as fundamental groups of $\\rm II_1$ factors (w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.06426","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"}