Intersectional pairs of $n$-knots, local moves of $n$-knots, and their associated invariants of $n$-knots. (arXiv:1803.03496v1 [math.GT])

Let n be an integer$>$. Let S^{n+2}_1 (respectively, S^{n+2}_2) be the (n+2)-sphere embedded in the (n+4)-sphere S^{n+4}. Let S^{n+2}_1 and S^{n+2}_2 intersect transversely. Suppose that the smooth submanifold, the intersection of S^{n+2}_1 and S^{n+2}_2 in S^{n+2}_i is PL homeomophic to the n-sphere. Then S^{n+2}_1 and S^{n+2}_2 in S^{n+2}_i is an n-knot K_i. We say that the pair (K_1,K_2) of n-knots is realizable. We consider the following problem in this paper. Let A_1 and A_2 be n-knots. Is the pair (A_1,A_2) of n-knots realizable? We give a complete characterization. 查看全文>>