Abstract
We construct a resolution of singularities for wave fronts having only stable singularities of corank 1. It is based on a transformation that takes a given front to a new front with singularities of the same type in a space of smaller dimension. This transformation is defined by the class Aµ of Legendre singularities. The front and the ambient space obtained by the Aµ-transformation inherit topological information on the closure of the manifold of singularities Aµ of the original front. The resolution of every (reducible) singularity of a front is determined by a suitable iteration of Aµ-transformations. As a corollary, we obtain new conditions for the coexistence of singularities of generic fronts.
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