[La topologie des multi-singularités de corank 1 des applications lisses et stables entre variétés de la même dimension]
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.
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@article{CRMATH_2005__340_6_441_0, author = {Sedykh, Vyacheslav D.}, title = {The topology of corank 1 multi-singularities of stable smooth mappings of equidimensional manifolds}, journal = {Comptes Rendus. Math\'ematique}, pages = {441--444}, publisher = {Elsevier}, volume = {340}, number = {6}, year = {2005}, doi = {10.1016/j.crma.2005.02.007}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2005.02.007/} }
TY - JOUR AU - Sedykh, Vyacheslav D. TI - The topology of corank 1 multi-singularities of stable smooth mappings of equidimensional manifolds JO - Comptes Rendus. Mathématique PY - 2005 SP - 441 EP - 444 VL - 340 IS - 6 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2005.02.007/ DO - 10.1016/j.crma.2005.02.007 LA - en ID - CRMATH_2005__340_6_441_0 ER -
%0 Journal Article %A Sedykh, Vyacheslav D. %T The topology of corank 1 multi-singularities of stable smooth mappings of equidimensional manifolds %J Comptes Rendus. Mathématique %D 2005 %P 441-444 %V 340 %N 6 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2005.02.007/ %R 10.1016/j.crma.2005.02.007 %G en %F CRMATH_2005__340_6_441_0
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://archive.numdam.org/articles/10.1016/j.crma.2005.02.007/
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