• Corpus ID: 232478878

0-Shake Slice Knots are Slice

@inproceedings{Akbulut20210ShakeSK,
  title={0-Shake Slice Knots are Slice},
  author={Selman Akbulut},
  year={2021}
}
Recall a knot K ⊂ S is called slice if it is the boundary of a properly imbedded smooth disk D ⊂ B. Let K = B + hK(r) be the 4manifold obtained by attaching a 2-handle to B along the knot K with framing r. Clearly K is slice if and only if K imbeds into S. We see this by writing S as two 4-balls B − ^ B 4 + glued along boundaries, and then using the slice disk in B + to imbed K 0 = B − + hK(0) ⊂ S. We say K is r-shake slice if a generator of H2(K ) = Z is represented by a smoothly imbedded 2… 

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References

On 2-dimensional homology classes of 4-manifolds
Let Kτ be a framed knot in S3 representing the 4-manifold which is obtained by attaching a 2-handle onto B4 along K with the framing τ (see (1)). Tristram (2) proved the following non-imbedding