{"paper":{"title":"Singular Seifert surfaces and Smale invariants for a family of 3-sphere immersions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GT","authors_text":"Masamichi Takase, Tobias Ekholm","submitted_at":"2009-03-02T09:04:22Z","abstract_excerpt":"A self-transverse immersion of the 2-sphere into 4-space with algebraic number of self intersection points equal to -n induces an immersion of the circle bundle over the 2-sphere of Euler class 2n into 4-space. Precomposing the circle bundle immersions with their universal covering maps, we get for n>0 immersions g_n of the 3-sphere into 4-space. In this note, we compute the Smale invariants of g_n. The computation is carried out by (partially) resolving the singularities of the natural singular map of the punctured complex projective plane which extends g_n.\n  As an application, we determine "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.0238","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"}