On 2-knots with total width eight

Abstract

A 2-knot is (the isotopy class of) a 2-sphere smoothly embedded in 4-space. The apparent contour of a generic planar projection of a 2-knot divides the plane into several regions, and to each such region, we associate the number of sheets covering it. The total width of a 2-knot is defined to be the minimum of the sum of these numbers, where we take the minimum among all generic planar projections of the given 2-knot. In this paper, we show that a 2-knot has total width eight if and only if it is an n-twist spun 2-bridge knot for some n≠±1.