Artículo
Geometric Objects and Cohomology Operations
Autor/es | González Díaz, Rocío
Real Jurado, Pedro |
Departamento | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) |
Fecha de publicación | 2012 |
Fecha de depósito | 2021-09-29 |
Publicado en |
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Resumen | Cohomology operations (including the cohomology ring) of a geometric object are finer
algebraic invariants than the homology of it. In the literature, there exist various algorithms
for computing the homology groups of ... Cohomology operations (including the cohomology ring) of a geometric object are finer algebraic invariants than the homology of it. In the literature, there exist various algorithms for computing the homology groups of simplicial complexes ([Mun84], [DE95,ELZ00], [DG98]), but concerning the algorithmic treatment of cohomology operations, very little is known. In this paper, we establish a version of the incremental algorithm for computing homology given in [ELZ00], which saves algebraic information, allowing us the computation of the cup product and the effective evaluation of the primary and secondary cohomology operations on the cohomology of a finite simplicial complex. The efficient combinatorial descriptions at cochain level of cohomology operations developed in [GR99,GR99a] are essential ingredients in our method. We study the computational complexity of these processes and a program in Mathematica for cohomology computations is presented. |
Agencias financiadoras | Junta de Andalucía Ministerio de Educación y Ciencia (MEC). España |
Identificador del proyecto | FQM-296
PB98–1621–C02–02 |
Cita | González Díaz, R. y Real Jurado, P. (2012). Geometric Objects and Cohomology Operations. ArXiv.org, arXiv:1206.4345 |