An n-component slice link is a link that bounds n disjoint discs in B^4. And the 4-genus of a link is defined to be the minimal genus of orientable surfaces bounded by it in B^4.


My question is: if the link bounds a surface with zero genus in B^4, is it necessarily a slice link? If not, any counter examples?



If the 4-genus of a link is zero, is it a slice link?
The Hopf link bounds a cylinder $S^1 \times [0,1]$ in $B^4$, and it's not slice since the two components have a non-zero linking number. 


