Deformations of maps on complete intersections, Damon’s KV -equivalence and bifurcations

A recent result of J. Damon’s [4] relates the Ae-versal unfoldings of a map-germ f with the KD(G)-versal unfoldings of an associated map germ which induces f from a stable map G. We extend this result to the case where the source is a complete intersection with an isolated singularity. In a similar vein, we also relate the bifurcation theoretic versal deformation of a bifurcation problem (map-germ) g to the K∆-versal deformation of an associated map germ which induces g from a versal deformation of the organizing centre g0 of g, where ∆ is the bifurcation set of this versal deformation. The extension of Damon’s theorem is used to provide an extension (again to cases where the source is an icis) of a result of Damon and Mond relating the discriminant Milnor number of a map to its Ae-codimension.