Movie moves for singular link cobordisms in 4-dimensional space

Abstract

Two singular links are cobordant if one can be obtained from the other by singular link isotopy together with a combination of births or deaths of simple unknotted curves, and saddle point transformations. A movie description of a singular link cobordism in 4-space is a sequence of singular link diagrams obtained from a projection of the cobordism into 3-space by taking 2-dimensional cross-sections perpendicular to a fixed direction. We present a set of movie moves that are sufficient to connect any two movies of isotopic singular link cobordisms.