Decomposing sphere system for a knot
= Decomposing sphere system for a knot
= Decomposing sphere systems for a knot
{synonym}
A finite collection of disjoint <splitting spheres of a knot> encodes a <connected sum of knots>. Cut along every <sphere> and fill each spherical boundary with a <three-ball> containing a straight arc joining its two marked endpoints. The resulting oriented <knots> are the factors. The system is complete when its nontrivial factors are <prime knots>.