[Sur les noyaux critiques]
Nous proposons une méthode pour rétracter homotopiquement des complexes simpliciaux. Pour cela nous introduisons la notion de face essentielle, et celle de noyau d'une cellule. Nous définissons alors le noyau critique d'un complexe. Notre principal résultat est que le noyau critique d'un complexe X est une rétraction homotopique de X. Nous généralisons ce résultat en donnant une condition nécessaire et suffisante qui caractérise une certaine classe de sous-complexes de X qui contiennent le noyau critique de X. En particulier, tout complexe qui appartient à cette classe est homotopiquement équivalent à X.
We propose a method for collapsing simplicial complexes. For that purpose, we introduce the notion of an essential face, and the one of a core of a cell. Then, we define the critical kernel of a complex. Our main result is that the critical kernel of a given complex X is a collapse of X. We extend this result by giving a necessary and sufficient condition which characterizes a certain class of subcomplexes of X which contain the critical kernel of X. In particular, any complex which belongs to this class is homotopy equivalent to X.
Accepté le :
Publié le :
Gilles Bertrand 1
@article{CRMATH_2007__345_7_363_0, author = {Gilles Bertrand}, title = {On critical kernels}, journal = {Comptes Rendus. Math\'ematique}, pages = {363--367}, publisher = {Elsevier}, volume = {345}, number = {7}, year = {2007}, doi = {10.1016/j.crma.2007.09.001}, language = {en}, }
Gilles Bertrand. On critical kernels. Comptes Rendus. Mathématique, Volume 345 (2007) no. 7, pp. 363-367. doi : 10.1016/j.crma.2007.09.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.09.001/
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