Regular-equivalence of 2-knot diagrams and sphere eversions

Abstract

AbstractFor each diagramDof a 2-knot, we provide a way to construct a new diagramD′ of the same knot such that any sequence of Roseman moves betweenDandD′ necessarily involves branch points. The proof is done by developing the observation that no sphere eversion can be lifted to an isotopy in 4-space.