{"paper":{"title":"A geometric classification of the path components of the space of locally stable maps $S^3\\to \\mathbb{R}^4$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.DG","authors_text":"Ole Andersson","submitted_at":"2013-12-13T20:59:14Z","abstract_excerpt":"Locally stable maps $S^3\\to\\mathbb{R}^4$ are classified up to homotopy through locally stable maps. The equivalence class of a map $f$ is determined by three invariants: the isotopy class $\\sigma(f)$ of its framed singularity link, the generalized normal degree $\\nu(f)$, and the algebraic number of cusps $\\kappa(f)$ of any extension of $f$ to a locally stable map of the $4$-disk into $\\mathbb{R}^5$. Relations between the invariants are described, and it is proved that for any $\\sigma$, $\\nu$, and $\\kappa$ which satisfy these relations, there exists a map $f:S^3\\to\\mathbb{R}^4$ with $\\sigma(f)="},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3940","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"}