Unknotting singular surface braids by crossing changes

Abstract

C.A. Giller defined a crossing change for surfaces in $4$-space, and proved an unknotting theorem. In this paper, we present such an unknotting theorem for singular surface braids, extending S. Kamada's result for those without branch points. As a consequence, we recover Giller's unknotting theorem. We also study finite type invariants for singular surface braids associated with the crossing changes.