Generators of the cohomology of $BV_3$

Kameko, Masaki

doi:10.1215/kjm/1250518069

Cited by 44 publications

(75 citation statements)

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“…(See Boardman [1], Bruner, Hà and Hưng [2], Carlisle and Wood [3], Crabb and Hubbuck [4], Giambalvo and Peterson [5], Hà [6], Hưng [7], Hưng and Nam [8,9], Hưng and Peterson [10,11], Janfada and Wood [12,13], Kameko [14,15], Minami [17], Mothebe [18,19], Nam [20,21], Repka and Selick [25], Silverman [26], Silverman and Singer [27], Singer [29], Walker and Wood [35,36,37], Wood [39,40] and others. )…”

Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

“…From the above equalities, we get γ i = 0, for i = 1, 2, 3, 4, 9, 10,11,12,15,16,17,18,19,24,42,43,46,53,54,55,56,57,58,59, 63, 64, 66 and γ 6 = γ 27 . γ 8 We need to show that γ 5 = γ 20 = γ 25 = γ 31 = 0.…”

Section: The Case Of Degreementioning

confidence: 96%

“…So, the condition d 1 The vector space QP 4 was also computed in Kameko [16] by using computer calculation. However the manuscript is unpublished at the time of the writing.…”

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confidence: 99%

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On the Peterson hit problem

Sum¹

2015

Advances in Mathematics

487

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Abstract. We study the hit problem, set up by F. Peterson, of finding a minimal set of generators for the polynomial algebra P k := F 2 [x 1 , x 2 , . . . , x k ] as a module over the mod-2 Steenrod algebra, A. In this paper, we study a minimal set of generators for A-module P k in some so-called generic degrees and apply these results to explicitly determine the hit problem for k = 4. Dedicated to Prof. N. H. V. Hưng on the occasion of his sixtieth birthday Introduction and statement of resultsLet V k be an elementary abelian 2-group of rank k. Denote by BV k the classifying space of V k . It may be thought of as the product of k copies of the real projective space RP ∞ . ThenHere the cohomology is taken with coefficients in the prime field F 2 of two elements.Being the cohomology of a space, P k is a module over the mod-2 Steenrod algebra A. The action of A on P k is explicitly given by the formulaand subject to the Cartan formulafor f, g ∈ P k (see Steenrod and Epstein [30]). A polynomial f in P k is called hit if it can be written as a finite sum f = i>0 Sq i (f i ) for some polynomials f i . That means f belongs to A + P k , where A + denotes the augmentation ideal in A. We are interested in the hit problem, set up by F. Peterson, of finding a minimal set of generators for the polynomial algebra P k as a module over the Steenrod algebra. In other words, we want to find a basis of the F 2 -vector spaceThe hit problem was first studied by Peterson [22,23]

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Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

Section: The Case Of Degreementioning

confidence: 96%

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On the Peterson hit problem

Sum¹

2015

Advances in Mathematics

487

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“…Au moment d'écrire ces lignes, nous avons appris que Kameko est en train de rédiger ses résultats complets [21] sur P A pour k = 4. En attendant, en vue de déterminer l'image du transfert algébrique quadruple, nous précisons la structure de GL-module de Γ A en degré pair pour k = 4.…”

Section: Annales De L'institut Fourierunclassified

Transfert algébrique et action du groupe linéaire sur les puissances divisées modulo 2

Nam

2008

Ann. inst. Fourier

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“…We shall also discuss how our action incorporates on the duals of the finite symmetric algebras the operators introduced by Kameko [11], Crossley [6], and Janfada and Wood [9; 10] (see also Hà [7]). …”

Section: Introduction and Theoremmentioning

confidence: 99%

A new action of the Kudo–Araki–May algebra on the dual of the symmetric algebras, with applications to the hit problem

Pengelley

Williams

2011

Algebr. Geom. Topol.

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A new action of the Kudo-Araki-May algebra on the dual of the symmetric algebras, with applications to the hit problem DAVID PENGELLEY FRANK WILLIAMSThe hit problem for a cohomology module over the Steenrod algebra A asks for a minimal set of A-generators for the module. In this paper we consider the symmetric algebras over the field F p , for p an arbitrary prime, and treat the equivalent problem of determining the set of A -primitive elements in their duals. We produce a method for generating new primitives from known ones via a new action of the Kudo-ArakiMay algebra K, and consider the K-module structure of the primitives, which form a sub K-algebra of the dual of the infinite symmetric algebra. Our examples show that the K-action on the primitives is not free. Our new action encompasses, on the finite symmetric algebras, the operators introduced by Kameko for studying the hit problem.

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Generators of the cohomology of $BV_3$

Cited by 44 publications

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On the Peterson hit problem

On the Peterson hit problem

Transfert algébrique et action du groupe linéaire sur les puissances divisées modulo 2

A new action of the Kudo–Araki–May algebra on the dual of the symmetric algebras, with applications to the hit problem

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