[The orchard cocycle]
We define and prove uniqueness of a natural homomorphism (called the Orchard morphism) from some groups associated naturally to a finite set E to the group of two-partitions of E representing equivalence relations having at most two classes on E. As an application, given a finite generic configuration , we exhibit a natural partition of in two sets.
Le but de cette Note est de montrer l'existence et l'unicité d'un homomorphisme naturel non-trivial entre certains groupes associés à un ensemble fini. Cet homomorphisme fournit une partition naturelle en deux sous-ensembles sur l'ensemble des points d'une configuration finie générique.
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Roland Bacher 1
@article{CRMATH_2004__338_3_187_0, author = {Roland Bacher}, title = {Le cocycle du verger}, journal = {Comptes Rendus. Math\'ematique}, pages = {187--190}, publisher = {Elsevier}, volume = {338}, number = {3}, year = {2004}, doi = {10.1016/j.crma.2003.11.021}, language = {fr}, }
Roland Bacher. Le cocycle du verger. Comptes Rendus. Mathématique, Volume 338 (2004) no. 3, pp. 187-190. doi : 10.1016/j.crma.2003.11.021. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2003.11.021/
[1] Chromatic properties of generic planar configurations of points (Preprint) | arXiv
[2] Topology and Geometry, Springer, 1993
[3] A Basic Course in Algebraic Topology, Springer, 1991
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