Geodesic
On the topology of stable corank 1 singularities on the boundary of a connected component of the complement to a front
Sbornik. Mathematics, Tome 195 (2004) no. 8, pp. 1165-1203 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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V. D. Sedykh. On the topology of stable corank 1 singularities on the boundary of a connected component of the complement to a front. Sbornik. Mathematics, Tome 195 (2004) no. 8, pp. 1165-1203. http://geodesic.mathdoc.fr/item/SM_2004_195_8_a2/

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