On Crossing Changes for Surface-Knots

Abstract

In this paper, we discuss the crossing change operation along exchangeable double curves of a surface-knot diagram. We show that under certain condition, a finite sequence of Roseman moves preserves the property of those exchangeable double curves. As an application for this result, we also define a numerical invariant for a set of surface-knots called $du$-exchangeable set.

References in corpus (1)

• Knotted surfaces and equivalencies of their diagrams without triple points