{"paper":{"title":"Zero sets of Lie algebras of analytic vector fields on real and complex 2-dimensional manifolds, II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"F.-J. Turiel, Morris W. Hirsch","submitted_at":"2016-06-27T15:35:59Z","abstract_excerpt":"On a real ($\\mathbb F=\\mathbb R$) or complex ($\\mathbb F=\\mathbb C$) analytic connected 2-manifold $M$ with empty boundary consider two vector fields $X,Y$. We say that $Y$ {\\it tracks} $X$ if $[Y,X]=fX$ for some continuous function $f\\colon M\\rightarrow\\mathbb F$. Let $K$ be a compact subset of the zero set ${\\mathsf Z}(X)$ such that ${\\mathsf\n  Z}(X)-K$ is closed, with nonzero Poincar\\'e-Hopf index (for example $K={\\mathsf Z}(X)$ when $M$ is compact and $\\chi(M)\\neq 0$) and let $\\mathcal G$ be a finite-dimensional Lie algebra of analytic vector fields on $M$. \\smallskip\n  {\\bf Theorem.} Let "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.08322","kind":"arxiv","version":1},"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"}