If the 4-genus of a link is zero, is it a slice link? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T08:31:13Z http://mathoverflow.net/feeds/question/14505 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/14505/if-the-4-genus-of-a-link-is-zero-is-it-a-slice-link If the 4-genus of a link is zero, is it a slice link? Megan 2010-02-07T16:18:53Z 2010-02-07T20:30:53Z <p>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.</p> <p>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?</p> http://mathoverflow.net/questions/14505/if-the-4-genus-of-a-link-is-zero-is-it-a-slice-link/14537#14537 Answer by Ryan Budney for If the 4-genus of a link is zero, is it a slice link? Ryan Budney 2010-02-07T19:09:36Z 2010-02-07T19:09:36Z <p>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. </p>