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-germf with the KD(G)-versal unfoldings of an associated map germ which induces ffrom a stable map G. We extend this result to the case where the source is acomplete intersection with an isolated singularity. In a similar vein, we also relatethe bifurcation theoretic versal deformation of a bifurcation problem (map-germ)g to the KV-versal deformation of an associated map germ which induces g from aversal deformation of the organizing centre g0 of g, where V is the bifurcation setof this versal deformation.The extension of Damon’s theorem is used to provide an extension (again tocases where the source is an icis) of a result of Damon and Mond relating thediscriminant Milnor number of a map to its Ae-codimension.