Asphericity results for ribbon disk complements via alternate descriptions

Abstract

An alternate description for ribbon disk complements in the $4$-ball is provided. It is known (and reestablished) that this description is equivalent to the standard LOT description, up to $3$-deformation. Amenable to geometric arguments, the alternate description yields asphericity results for ribbon disk complements using simple graph-theoretic criteria and, later, using a relative homotopy group which arises naturally. In the course of making and modifying the description, two algorithms are given for presenting ribbon disk groups.