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Computing Cocycles on Simplicial Complexes
"... In this note, working in the context of simplicial sets [17], we give a detailed study of the complexity for computing chain level Steenrod squares [20,21], in terms of the number of face operators required. This analysis is based on the combinatorial formulation given in [5]. As an application, we ..."
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Cited by 3 (1 self)
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In this note, working in the context of simplicial sets [17], we give a detailed study of the complexity for computing chain level Steenrod squares [20,21], in terms of the number of face operators required. This analysis is based on the combinatorial formulation given in [5]. As an application, we give here an algorithm for computing cupi products over integers on a simplicial complex at chain level. 1
On the Cohomology of Central Frattini Extensions
 Journal of Pure and Applied Algebra
, 2001
"... Abstract. In this paper we provide calculations for the mod p cohomology of certain p–groups, using topological methods. More precisely, we look at pgroups G defined as central extensions 1 → V → G → W → 1 of elementary abelian groups such that G/[G, G]⊗Fp = W and the defining k–invariants span the ..."
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Cited by 3 (2 self)
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Abstract. In this paper we provide calculations for the mod p cohomology of certain p–groups, using topological methods. More precisely, we look at pgroups G defined as central extensions 1 → V → G → W → 1 of elementary abelian groups such that G/[G, G]⊗Fp = W and the defining k–invariants span the entire image of the Bockstein. We show that if p> dim V − dim W + 1, then the mod p cohomology of G can be explicitly computed as an algebra of the form P ⊗ A where P is a polynomial ring on 2dimensional generators and A is the cohomology of a compact manifold which in turn can be computed as the homology of a Koszul complex. As an application we provide a complete determination of the mod p cohomology of the universal central extension 1 → H2 (W, Fp) → U → W → 1 provided p> () n 2 + 1, where n = dim W.
unknown title
, 1999
"... Analyzing the transference of the coalgebra structure on the homology of CDGAs ..."
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Analyzing the transference of the coalgebra structure on the homology of CDGAs
"Coalgebra" Structures on 1Homological Models for Commutative Differential Graded Algebras
"... In [3] "mall" 1homological model H of a commutative differential graded algebra is described. Homological Perturbation Theory (HPT) [79] provides an explicit description of an A1coalgebra structure ( 1 ; 2 ; 3 ; : : :) of H. In this paper, we are mainly interested in the determination of the map ..."
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In [3] "mall" 1homological model H of a commutative differential graded algebra is described. Homological Perturbation Theory (HPT) [79] provides an explicit description of an A1coalgebra structure ( 1 ; 2 ; 3 ; : : :) of H. In this paper, we are mainly interested in the determination of the map 2 : H ! H H as a first step in the study of this structure. Developing the techniques given in [20] (inversion theory), we get an important improvement in the computation of 2 with regard to the first formula given by HPT. In the case of purely quadratic algebras, we sketch a procedure for giving the complete Hopf algebra structure of its 1homology.
Rocío González–Díaz, Pedro Real Universidad de Sevilla, Depto. de Matemática Aplicada I,
, 2001
"... In this note, working in the context of simplicial sets [17], we give a detailed study of the complexity for computing chain level Steenrod squares [20, 21], in terms of the number of face operators required. This analysis is based on the combinatorial formulation given in [5]. As an application, we ..."
Abstract
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In this note, working in the context of simplicial sets [17], we give a detailed study of the complexity for computing chain level Steenrod squares [20, 21], in terms of the number of face operators required. This analysis is based on the combinatorial formulation given in [5]. As an application, we give here an algorithm for computing cup–i products over integers on a simplicial complex at chain level. 1