{"paper":{"title":"Manifolds which admit maps with finitely many critical points into spheres of small dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Cornel Pintea, Louis Funar","submitted_at":"2016-11-14T11:30:04Z","abstract_excerpt":"We construct, for $m\\geq 6$ and $2n\\leq m$, closed manifolds $M^{m}$ with finite nonzero $\\varphi(M^{m},S^{n}$), where $\\varphi(M,N)$ denotes the minimum number of critical points of a smooth map $M\\to N$. We also give some explicit families of examples for even $m\\geq 6, n=3$, taking advantage of the Lie group structure on $S^3$. Moreover, there are infinitely many such examples with $\\varphi(M^{m},S^{n})=1$. Eventually we compute the signature of the manifolds $M^{2n}$ occurring for even $n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04344","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"}