{"paper":{"title":"The intersection of three spheres in a sphere and a new application of the Sato-Levine invariant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Eiji Ogasa","submitted_at":"2018-03-10T17:37:59Z","abstract_excerpt":"Take transverse immersions f from a disjoint unin of the three 4-spheres $S^4_1$, $S^4_2$, and $S^4_3$ into $S^6$ with the following properties:\n  (1) The restriction of $f$ to $S^4_i$ is an embedding,\n  (2) The intersection of $f(S^4_i)$ and $f(S^4_j)$ is not empty and connected,\n  (3)The intersection among $f(S^4_1)$, $f(S^4_2)$, and $f(S^4_3)$ is not empty.\n  Then we obtain three surface-links $L_i=(S^4_i\\cap S^4_j, S^4_i\\cap S^4_k)$ in $S^4_i$, where $(i,j,k)=(1,2,3), (2,3,1), (3,1,2).$ We prove that, we have the equality $\\beta(L_1)+\\beta(L_2)+\\beta(L_3)=0$, where $\\beta(L_i)$ is the Sato"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03843","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"}