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A cubical model of a fibration
 J. Pure Appl. Algebra
"... Abstract. In the paper the notion of a truncating twisting function from a simplicial set to a cubical set and the corresponding notion of twisted Cartesian product of these sets are introduced. The latter becomes a cubical set. This construction together with the theory of twisted tensor products f ..."
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Abstract. In the paper the notion of a truncating twisting function from a simplicial set to a cubical set and the corresponding notion of twisted Cartesian product of these sets are introduced. The latter becomes a cubical set. This construction together with the theory of twisted tensor products for homotopy Galgebras allows to obtain multiplicative models for fibrations. 1.
Computing Resolutions over Finite pGroups
, 2000
"... . A uniform and constructive approach for the computation of resolutions and for (co)homology computations for any nite pgroup is detailed. The resolutions we construct ([32]) are, as vector spaces, as small as the minimal resolution of IFp over the elementary abelian pgroup of the same order as t ..."
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Cited by 3 (0 self)
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. A uniform and constructive approach for the computation of resolutions and for (co)homology computations for any nite pgroup is detailed. The resolutions we construct ([32]) are, as vector spaces, as small as the minimal resolution of IFp over the elementary abelian pgroup of the same order as the group under study. Our implementations are based on the development of sophisticated algebraic data structures. Applications to calculating functional cocycles are given and the possibility of constructing interesting codes using such methods is presented. 1 Introduction In this paper, we present a uniform constructive approach to calculating relatively small resolutions over nite pgroups. The algorithm we use comes from [32, 8.1.8 and the penultimate paragraph of 9.4]. There has been a massive amount of work done on the structure of pgroups since the beginning of group theory. A good introduction is [22]. We combine mathematical and computer methods to construct the uniform resolut...
The twisted Cartesian model for the double path space fibration
"... Abstract. The paper introduces the notion of a truncating twisting function from a cubical set to a permutahedral set and the corresponding notion of twisted Cartesian product of these sets. The latter becomes a permutocubical set that models in particular the path space fibration on a loop space. T ..."
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Abstract. The paper introduces the notion of a truncating twisting function from a cubical set to a permutahedral set and the corresponding notion of twisted Cartesian product of these sets. The latter becomes a permutocubical set that models in particular the path space fibration on a loop space. The chain complex of this twisted Cartesian product in fact is a comultiplicative twisted tensor product of cubical chains of base and permutahedral chains of fibre. This construction is formalized as a theory of twisted tensor products for Hirsch algebras. 1. introduction The paper continues [12] in which a combinatorial model for a fibration was constructed based on the notion of a truncating twisting function from a simplicial set to a cubical set and on the corresponding notion of twisted Cartesian product of these sets being a cubical set. Applying the cochain functor we obtain a multiplicative twisted tensor product modeling the corresponding fibration. There arises a need to iterate this construction for fibrations over loop or path
"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 o ..."
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Cited by 1 (1 self)
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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.
Homological Computations for pGroups
"... A uniform and constructive approach for the computation of resolutions and for (co)homology computations for any nite pgroup is detailed. The resolutions we construct ([29]) are, as vector spaces, as small as the minimal resolution of IFp over the elementary abelian pgroup of the same order as the ..."
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A uniform and constructive approach for the computation of resolutions and for (co)homology computations for any nite pgroup is detailed. The resolutions we construct ([29]) are, as vector spaces, as small as the minimal resolution of IFp over the elementary abelian pgroup of the same order as the group under study. Our implementations are based on the development of sophisticated algebraic data structures. Applications to calculating functional cocycles are given and the possibility of constructing interesting codes using such methods is presented. 1