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

Sedykh, Vyacheslav D.1
1 Department of Higher Mathematics, Russian State University of Oil and Gas (Gubkin), Leninsky prosp. 65, Moscow 119991, Russia
Comptes Rendus. Mathématique, Tome 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
Sedykh, Vyacheslav D. 1

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

[1] Arnold, V.I.; Vassiliev, V.A.; Goryunov, S.M.; Lyashko, O.V. Singularities 1. Local and Global Theory, Springer, Berlin, 1993

[2] Goryunov, V.; Mond, D. Vanishing cohomology of singularities of mappings, Compos. Math., Volume 89 (1993), pp. 45-80

[3] Kazarian, M.E. Multi-singularities, cobordisms and enumerative geometry, Uspekhi Mat. Nauk, Volume 58 (2003) no. 4, pp. 29-88

[4] Kleiman, S.L. Multiple-point formulas I: Iteration, Acta Math., Volume 147 (1981) no. 1–2, pp. 13-49

[5] Marar, W.L.; Mond, D. Multiple-point schemes for corank 1 maps, J. London Math. Soc. (2), Volume 39 (1989) no. 3, pp. 553-567

[6] McCrory, C.; Parusiński, A. Algebraically constructible functions, Ann. Sci. École Norm. Sup. (4), Volume 30 (1997) no. 4, pp. 527-552

[7] Morin, B. Formes canoniques des singularités d'une application différentiable, C. R. Acad. Sci. Paris, Volume 260 (1965), pp. 5662-5665

[8] Romero Fuster, M.C. Sphere stratifications and the Gauss map, Proc. Roy. Soc. Edinburgh Sect. A, Volume 95 (1983), pp. 115-136

[9] Sedykh, V.D.; Sedykh, V.D. Resolution of corank 1 singularities of a generic front, Funktsional. Anal. i Prilozhen, Volume 37 (2003) no. 2, pp. 52-64 (English translation in Funct. Anal. Appl., 37, 2, 2003, pp. 123-133)

[10] Sedykh, V.D.; Sedykh, V.D. 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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