Geodesic
On the Coexistence of Corank~1 Multisingularities of a~Stable Smooth Mapping of Equidimensional Manifolds
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analysis and singularities. Part 1, Tome 258 (2007), pp. 201-226

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We study the topology of stable smooth mappings of smooth closed real manifolds of the same dimension. We calculate all universal linear relations between the Euler characteristics of the manifolds of multisingularities of mappings that have only corank 1 singularities. 
@article{TM_2007_258_a13,
     author = {V. D. Sedykh},
     title = {On the {Coexistence} of {Corank~1} {Multisingularities} of {a~Stable} {Smooth} {Mapping} of {Equidimensional} {Manifolds}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {201--226},
     publisher = {mathdoc},
     volume = {258},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2007_258_a13/}
}
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V. D. Sedykh. On the Coexistence of Corank~1 Multisingularities of a~Stable Smooth Mapping of Equidimensional Manifolds. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analysis and singularities. Part 1, Tome 258 (2007), pp. 201-226. http://geodesic.mathdoc.fr/item/TM_2007_258_a13/