Geodesic
On the Coexistence of Corank~1 Multisingularities of a~Stable Smooth Mapping of Equidimensional Manifolds
Informatics and Automation, 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{TRSPY_2007_258_a13,
     author = {V. D. Sedykh},
     title = {On the {Coexistence} of {Corank~1} {Multisingularities} of {a~Stable} {Smooth} {Mapping} of {Equidimensional} {Manifolds}},
     journal = {Informatics and Automation},
     pages = {201--226},
     publisher = {mathdoc},
     volume = {258},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_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. Informatics and Automation, Analysis and singularities. Part 1, Tome 258 (2007), pp. 201-226. http://geodesic.mathdoc.fr/item/TRSPY_2007_258_a13/