On primitive sets of loops in the boundary of a handlebody
It is shown that a collection \(\{J_ 1,J_ 2,...\}\) of pairwise disjoint simple closed curves in the boundary of a 3-dimensional handlebody, X, is primitive if and only if for each subcollection of the curves the 3-manifold obtained by attaching 2-handles to X along the curves of the subcollection is a handlebody. Being primitive means that there is a collection \(\{D_ 1,D_ 2,...\}\) of pairwise disjoint, properly embedded 2-cells in X which are transverse to \(\{J_ 1,J_ 2,...\}\) and with \(| J_ i\cap D_ j| =\delta_{ij}\).
pairwise disjoint simple closed curves in the boundary of a 3-dimensional handlebody
scientific article; zbMATH DE number 4032623