On a genus of a closed surface containing a Brunnian link
A link in the 3-sphere is called Brunnian if it is nontrivial but any sub-link obtained by removing a single component is trivial. In the paper under review, the author shows that if a Brunnian link of \(n\) components is isotoped so that it is contained in a closed embedded surface in the 3-sphere, then the genus of the surface is greater than \((n+3)/3\). A key lemma for the proof is the existence of a certain essential tangle decomposition for a Brunnian link, which is of interest independently. Using this lemma, the main result is proved via cut-and-paste techniques in a smart way. Also stated is a conjecture that the bound could be sharpened so that the genus of such a surface is greater than just \(n\).
scientific article; zbMATH DE number 5545417