ribbon links - counterexamples - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T03:16:20Z http://mathoverflow.net/feeds/question/42293 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/42293/ribbon-links-counterexamples ribbon links - counterexamples Paolo Aceto 2010-10-15T14:40:02Z 2010-10-29T00:08:48Z <p>An n-component link is said to be ribbon if it bounds a ribbon surface consisting of n discs. (a ribbon surface is an immersed surface with only ribbon singularities, see <a href="http://en.wikipedia.org/wiki/Ribbon_knot" rel="nofollow">http://en.wikipedia.org/wiki/Ribbon_knot</a>).</p> <p>Let \$L=L_1\cup,...,\cup L_n\$ be an n-component link (n>1). The following conditions are necessary for L to be ribbon:</p> <ul> <li>for each pair \$(L_i,L_j)\$ we have \$lk(L_i,L_j)=0\$ (lk=linking number)</li> <li>each \$L_i\$ is itself a ribbon knot</li> <li>Let V(L) be the Jones Polynomial of L and \$V(O^n)\$ be the Jones polynomial of the trivial n-component link then \$V(O^n)\$ is a factor of V(L) i.e. \$V(O^n)|V(L)\$ (Eisermann arxiv.org/abs/0802.2287)</li> </ul> <p>My questions are:</p> <ul> <li><p>Is there any example of a link which is not ribbon satisfying the previous conditions?</p></li> <li><p>Are there any other necessary conditions?</p></li> </ul>