{"paper":{"title":"Smooth toric actions are described by a single vector field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.RT"],"primary_cat":"math.DG","authors_text":"A. Viruel, F.J. Turiel","submitted_at":"2015-09-14T14:41:00Z","abstract_excerpt":"Consider a smooth effective action of a torus $\\mathbb{T}^n$ on a connected $C^{\\infty}$-manifold $M$ of dimension $m$. Then $n\\leq m$. In this work we show that if $n<m$, then there exist a complete vector field $X$ on $M$ such that the automorphism group of $X$ equals $\\mathbb T^n \\otimes \\mathbb{R}$, where the factor $\\mathbb{R}$ comes from the flow of $X$ and $\\mathbb{T}^n$ is regarded as a subgroup of the full group of diffeomorphisms of ${\\operatorname{Diff}}(M)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.04118","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"}