Artículo
Cups products in Z2-cohomology of 3D polyhedral complexes
Autor/es | González Díaz, Rocío
Lamar León, Javier Umble, Ronald |
Departamento | Universidad de Sevilla. Departamento de Matemática Aplicada I |
Fecha de publicación | 2012 |
Fecha de depósito | 2015-11-18 |
Publicado en |
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Resumen | Let I=(Z3,26,6,B) be a 3D digital image, let Q(I) be the associated cubical complex and let ∂Q(I) be the subcomplex of Q(I) whose maximal cells are the quadrangles of Q(I) shared by a voxel of B in the foreground -- the ... Let I=(Z3,26,6,B) be a 3D digital image, let Q(I) be the associated cubical complex and let ∂Q(I) be the subcomplex of Q(I) whose maximal cells are the quadrangles of Q(I) shared by a voxel of B in the foreground -- the object under study -- and by a voxel of Z3∖B in the background -- the ambient space. We show how to simplify the combinatorial structure of ∂Q(I) and obtain a 3D polyhedral complex P(I) homeomorphic to ∂Q(I) but with fewer cells. We introduce an algorithm that computes cup products on H∗(P(I);Z2) directly from the combinatorics. The computational method introduced here can be effectively applied to any polyhedral complex embedded in R3. |
Ficheros | Tamaño | Formato | Ver | Descripción |
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Cups products in Z.pdf | 1.033Mb | [PDF] | Ver/ | |