Comptes Rendus
no. 6
Differential Topology/Differential Geometry
The topology of corank 1 multi-singularities of stable smooth mappings of equidimensional manifolds
[La topologie des multi-singularités de corank 1 des applications lisses et stables entre variétés de la même dimension]

Présenté par : Vladimir I. Arnol'd

Vyacheslav D. Sedykh1
1 Department of Higher Mathematics, Russian State University of Oil and Gas (Gubkin), Leninsky prosp. 65, Moscow 119991, Russia
Comptes Rendus. Mathématique, Volume 340 (2005) no. 6, pp. 441-444.

Nous étudions des conditions pour la co-existence de singularités d'une application lisse et stable d'une variété fermée dans une variété de la même dimension n. Sous l'hypothèse de que cette application a seulement des singularités de corank 1, nous obtenons relations linéaires universelles entre les nombres d'Euler des variétés de multi-singularités dans l'image de cette application.

We study conditions for the coexistence of singularities of a stable smooth mapping of a closed manifold into a manifold of the same dimension n. Assuming that this mapping has only singularities of corank 1, we find universal linear relations between the Euler characteristics of the manifolds of multi-singularities in the image of the considered mapping.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2005.02.007
Vyacheslav D. Sedykh 1

1 Department of Higher Mathematics, Russian State University of Oil and Gas (Gubkin), Leninsky prosp. 65, Moscow 119991, Russia 
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Vyacheslav D. Sedykh. The topology of corank 1 multi-singularities of stable smooth mappings of equidimensional manifolds. Comptes Rendus. Mathématique, Volume 340 (2005) no. 6, pp. 441-444. doi : 10.1016/j.crma.2005.02.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.02.007/

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[10] V.D. Sedykh; V.D. Sedykh On the topology of the image of a stable smooth mapping with singularities of corank 1, Dokl. Akad. Nauk, Volume 395 (2004) no. 4, pp. 459-463 (English translation in Russian Acad. Sci. Dokl. Math., 69, 2, 2004, pp. 235-239)

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