If the fundamental group of the complement of a smooth embedding
f:S2⊂R4 is a cyclic group, the map
can be deformed to the standard embedding by a generic one-parameter
family with at most cusp singularities. If two smooth embeddings are
connected by such a deformation, they will be called cusp equivalent. We
will discuss the relation of three equivalences of smooth 2–knots
S2⊂R4; cusp equivalence, stable
equivalence and weakly stable equivalence.
Keywords
cusp, generic deformation of maps, smooth
2–knots, stable equivalence