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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","authors_text":"Eiji Ogasa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-03-10T17:37:59Z","title":"The intersection of three spheres in a sphere and a new application of the Sato-Levine 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