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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?

edited Feb 7 2010 at 20:30

Ryan Budney
21.8k●1●41●102

asked Feb 7 2010 at 16:18

Megan
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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 2010 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 2010 at 18:57

Ryan Budney · Accepted Answer · 2010-02-07 19:09:36Z UTC

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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.

answered Feb 7 2010 at 19:09

Ryan Budney
21.8k●1●41●102

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

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