{"paper":{"title":"Automorphisms of generic gradient vector fields with prescribed finite symmetries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.DG","authors_text":"Ignasi Mundet i Riera","submitted_at":"2017-03-20T16:46:56Z","abstract_excerpt":"Let $M$ be a compact and connected smooth manifold endowed with a smooth action of a finite group $\\Gamma$, and let $f$ be a $\\Gamma$-invariant Morse function on $M$. We prove that the space of $\\Gamma$-invariant Riemannian metrics on $M$ contains a residual subset ${\\mathcal Met}_f$ with the following property. Let $g\\in{\\mathcal Met}_f$ and let $\\nabla^gf$ be the gradient vector field of $f$ with respect to $g$. For any diffeomorphism $\\phi$ of $M$ preserving $\\nabla^gf$ there exists some real number $t$ and some $\\gamma\\in\\Gamma$ such that for every $x\\in M$ we have $\\phi(x)=\\gamma\\,\\Phi_t^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.06837","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"}