# If the 4-genus of a link is zero, is it a slice link?

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?

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Since as of your last question, you were sure of the difference between these, your question would probably be a lot more helpful to others if you included the definitions in the question. –  Ben Webster Feb 7 '10 at 16:28
Thanks. And I realize the initial question was a stupid one. I edited it and think this one is the one I really wanna ask. –  Megan Feb 7 '10 at 18:57
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.