Results 1  10
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13
A combinatorial method for computing Steenrod squares
, 1999
"... We present here a combinatorial method for computing Steenrod squares of a simplicial set X . This method is essentially based on the determination of explicit formulae for the component morphisms of a higher diagonal approximation (i.e., a family of morphisms measuring the lack of commutativity of ..."
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We present here a combinatorial method for computing Steenrod squares of a simplicial set X . This method is essentially based on the determination of explicit formulae for the component morphisms of a higher diagonal approximation (i.e., a family of morphisms measuring the lack of commutativity of the cup product on the cochain level) in terms of face operators of X.A generalization of this method to Steenrod reduced powers is sketched. c 1999 Elsevier Science B.V. All rights reserved.
Universal classes for algebraic groups
"... Abstract. We exhibit cocycles representing certain classes in the cohomology of the algebraic group GLn with coefficients in the representation Γ ∗ (gl (1) n). These classes ’ existence was anticipated by van der Kallen, and they intervene in the proof that reductive linear algebraic groups have fin ..."
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Cited by 3 (2 self)
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Abstract. We exhibit cocycles representing certain classes in the cohomology of the algebraic group GLn with coefficients in the representation Γ ∗ (gl (1) n). These classes ’ existence was anticipated by van der Kallen, and they intervene in the proof that reductive linear algebraic groups have finitely generated cohomology algebras [18]. Let�be a field of positive characteristic, let A be a finitely generated �algebra, and let G be a reductive linear algebraic group defined over� and acting rationally on A by algebra automorphisms. Then the rational cohomology H ∗ (G,A) is an algebra, and one can wonder if it is finitely generated. In degree 0, the finite generation of the subalgebra AG = H0 (G,A) is part of Hilbert’s fourteenth problem and was solved positively by the work of Nagata [13] and Haboush [9]. The finite generation of the whole cohomology algebra remained unsolved in general, though much progress had been made in recent years [7, 20].
On the computability of the plocal homology of twisted cartesian products of EilenbergMac Lane spaces
, 1999
"... Working in the framework of the Simplicial Topology, a method for calculating the plocal homology of a twisted cartesian product X(#, m, #, # # , n) = K(#, m) # K(# # , n) of EilenbergMac Lane spaces is given. The chief technique is the construction of an explicit homotopy equivalence between the ..."
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Cited by 1 (1 self)
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Working in the framework of the Simplicial Topology, a method for calculating the plocal homology of a twisted cartesian product X(#, m, #, # # , n) = K(#, m) # K(# # , n) of EilenbergMac Lane spaces is given. The chief technique is the construction of an explicit homotopy equivalence between the normalized chain complex of X and a free DGAmodule of finite type M , via homological perturbation. If X is a commutative simplicial group (being its inner product the natural one of the cartesian product of K(#, m) and K(# # , n)), then M is a DGAalgebra. Finally, in the special case K(#, 1) ## X K(# # , n), we prove that M can be a small twisted tensor product. 1
Simplicial Perturbation Techniques and Effective Homology
"... In this paper, we deal with the problem of the computation of the homology of a finite simplicial complex after an "elementary simplicial perturbation" process such as the inclusion or elimination of a maximal simplex or an edge contraction. To this aim we compute an algebraic topological model that ..."
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In this paper, we deal with the problem of the computation of the homology of a finite simplicial complex after an "elementary simplicial perturbation" process such as the inclusion or elimination of a maximal simplex or an edge contraction. To this aim we compute an algebraic topological model that is an special chain homotopy equivalence connecting the simplicial complex with its homology (working with a field as the ground ring).
A survey of Huebschmann and Stasheff’s paper: Formal solution of the master equation via HPT and deformation theory, math.QA/0704.0432v1
, 2007
"... These notes, based on the paper [8] by Huebschmann and Stasheff, were prepared for a series of talks at Illinois State University with the intention of applying ..."
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Cited by 1 (1 self)
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These notes, based on the paper [8] by Huebschmann and Stasheff, were prepared for a series of talks at Illinois State University with the intention of applying
"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.
Computing "Small" 1Homological Models for Commutative Differential Graded Algebras
"... We use homological perturbation machinery specific for the algebra category [13] to give an algorithm for computing the differential structure of a small 1homological model for commutative differential graded algebras (briefly, CDGAs). The complexity of the procedure is studied and a computer packa ..."
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We use homological perturbation machinery specific for the algebra category [13] to give an algorithm for computing the differential structure of a small 1homological model for commutative differential graded algebras (briefly, CDGAs). The complexity of the procedure is studied and a computer package in Mathematica is described for determining such models.
An Algorithm for Computing Cocyclic Matrices Developed Over Some Semidirect Products
"... An algorithm for calculating a set of generators of representative 2cocycles on semidirect product of finite abelian groups is constructed, in light of the theory over cocyclic matrices developed by Horadam and de Launey in [7, 8]. The method involves some homological perturbation techniques [3, 1] ..."
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An algorithm for calculating a set of generators of representative 2cocycles on semidirect product of finite abelian groups is constructed, in light of the theory over cocyclic matrices developed by Horadam and de Launey in [7, 8]. The method involves some homological perturbation techniques [3, 1], in the homological correspondent to the work which Grabmeier and Lambe described in [12] from the viewpoint of cohomology. Examples of explicit computations over all dihedral groups D4t are given, with aid of Mathematica. 1
Homology, Homotopy and Applications, vol.5(2), 2003, pp.8393
 Homology, Homotopy and Applications
, 2003
"... We propose a method for calculating cohomology operations on finite simplicial complexes. ..."
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We propose a method for calculating cohomology operations on finite simplicial complexes.
Computing Adem Cohomology Operations
, 2006
"... We deal with the problem of obtaining explicit simplicial formulae defining the classical Adem cohomology operations at the cochain level. Having these formulae at hand, we design an algorithm for computing these operations for any finite simplicial set. ..."
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We deal with the problem of obtaining explicit simplicial formulae defining the classical Adem cohomology operations at the cochain level. Having these formulae at hand, we design an algorithm for computing these operations for any finite simplicial set.