I am reading the paper,ON ATTACHING 3-HANDLES TO A 1-CONNECTED 4-MANIFOLD by BRUCE TRACE here.He says in this paper that we need only construct a knot $K\subset \partial W^4$ which meets $Σ ^2$ transversely in a single point (i.e., $K$ and $Σ ^2$ are complementary in $\partial W ^4$ ) ,where $W^4$ is 1-connected smooth 4-manifold and $Σ^2$ is 2-sphere in $\partial W^4$.I read this and I can't understand this because I think that $K$ have at least two points in which $K$ intersects $\ Σ^2$. If you can understand why we take such a knot $K$ and find the point of my misunderstanding this ,could you teach me the reason for the existence of $K$ and correct me?
A knot which intersects $S^2$ transversely once in 3-connected manifold
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