On the topology of stable corank 1 singularities on the boundary of a connected component of the complement to a front

Abstract

Constraints on the position of singularities on the boundary of a connected component of the complement to a wave front are studied. The boundary of the component is assumed to be the compact boundary of a manifold, and the front is assumed to have only stable corank 1 singularities at points of the boundary. Under these assumptions linear relations are found between the Euler numbers of the manifolds of singularities on the boundary of a fixed component. In particular, all universal linear relations between the Euler numbers of the manifolds of singularities on the boundaries of elliptic and hyperbolic connected components of the complement to a front are found.