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Problems in the Steenrod algebra
 Bull. London Math. Soc
, 1998
"... This article contains a collection of results and problems about the Steenrod algebra and related algebras acting on polynomials which nonspecialists in topology may find of some interest. Although there are topological allusions throughout the article, the emphasis is on the algebraic development ..."
Abstract

Cited by 30 (1 self)
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This article contains a collection of results and problems about the Steenrod algebra and related algebras acting on polynomials which nonspecialists in topology may find of some interest. Although there are topological allusions throughout the article, the emphasis is on the algebraic development of the Steenrod algebra and its connections to the various topics indicated below. Contents 1 Historical background 4
Differential Operators and the Steenrod Algebra
, 1995
"... This article presents an elementary treatment of the Steenrod algebra from an algebraic point of view in terms of differential operators acting on polynomials. The exposition concentrates on the Steenrod algebra A over the field F 2 of two elements although the approach works for the odd prime field ..."
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Cited by 9 (3 self)
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This article presents an elementary treatment of the Steenrod algebra from an algebraic point of view in terms of differential operators acting on polynomials. The exposition concentrates on the Steenrod algebra A over the field F 2 of two elements although the approach works for the odd prime fields. From a
Spherical classes and the algebraic transfer
 Trans. Amer. Math. Soc
"... Abstract. We study a weak form of the classical conjecture which predicts that there are no spherical classes in Q0S0 except the elements of Hopf invariant one and those of Kervaire invariant one. The weak conjecture is obtained by restricting the Hurewicz homomorphism to the homotopy classes which ..."
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Cited by 8 (2 self)
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Abstract. We study a weak form of the classical conjecture which predicts that there are no spherical classes in Q0S0 except the elements of Hopf invariant one and those of Kervaire invariant one. The weak conjecture is obtained by restricting the Hurewicz homomorphism to the homotopy classes which are detected by the algebraic transfer. Let Pk = F2[x1; : : : ; xk] with jxij = 1. The general linear group GLk = GL(k;F2) and the (mod 2) Steenrod algebra A act on Pk in the usual manner. We prove that the weak conjecture is equivalent to the following one: The canonical homomorphism jk: F2 A
Spherical classes and the Dickson algebra
, 1996
"... We attack the conjecture that the only spherical classes in the homology of Q 0 S 0 are Hopf invariant one and Kervaire invariant one elements. We do this by computing products in the E 2 term of the unstable Adams spectral sequence converging to (Q 0 S 0 ) using results about the Dickson ..."
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Cited by 7 (3 self)
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We attack the conjecture that the only spherical classes in the homology of Q 0 S 0 are Hopf invariant one and Kervaire invariant one elements. We do this by computing products in the E 2 term of the unstable Adams spectral sequence converging to (Q 0 S 0 ) using results about the Dickson algebra and by studying the LannesZarati homomorphism.
Sheared algebra maps and operation bialgebras for mod 2 homology and cohomology
 Trans. Amer. Math. Soc
"... Abstract. The mod 2 Steenrod algebra A and DyerLashof algebra R have both striking similarities and dierences, arising from their common origins in \lowerindexed " algebraic operations. These algebraic operations and their relations generate a bigraded bialgebra K, whose module actions are e ..."
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Cited by 7 (6 self)
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Abstract. The mod 2 Steenrod algebra A and DyerLashof algebra R have both striking similarities and dierences, arising from their common origins in \lowerindexed " algebraic operations. These algebraic operations and their relations generate a bigraded bialgebra K, whose module actions are equivalent to, but quite different from, those of A and R. The exact relationships emerge as \sheared algebra bijections", which also illuminate the role of the cohomology of K. As a bialgebra, K has a particularly attractive and potentially useful structure, providing a bridge between those of A and R, and suggesting possible applications to the Miller spectral sequence and the A structure of Dickson algebras. 1.
Contents
"... This article contains a collection of results and problems about the Steenrod algebra and related algebras acting on polynomials which nonspecialists in topology may nd of some interest. Although there are topological allusions throughout the article, the emphasis is on the algebraic development of ..."
Abstract
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This article contains a collection of results and problems about the Steenrod algebra and related algebras acting on polynomials which nonspecialists in topology may nd of some interest. Although there are topological allusions throughout the article, the emphasis is on the algebraic development of the Steenrod algebra and its connections to the various topics indicated below.
'k: Ext
"... Dedicated to Professor Nguyê~n Duy Tiên on the occasion of his sixtieth birthday Abstract. Let A be the mod 2 Steenrod algebra and Dk the Dickson algebra of k variables. We study the LannesZarati homomorphisms ..."
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Dedicated to Professor Nguyê~n Duy Tiên on the occasion of his sixtieth birthday Abstract. Let A be the mod 2 Steenrod algebra and Dk the Dickson algebra of k variables. We study the LannesZarati homomorphisms
Spherical classes and the Dickson algebra
, 1996
"... We attack the conjecture that the only spherical classes in the homology of Q0S 0 are Hopf invariant one and Kervaire invariant one elements. We do this by computing products in the E2term of the unstable Adams spectral sequence converging to (Q0S0) using results about the Dickson algebra and by st ..."
Abstract
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We attack the conjecture that the only spherical classes in the homology of Q0S 0 are Hopf invariant one and Kervaire invariant one elements. We do this by computing products in the E2term of the unstable Adams spectral sequence converging to (Q0S0) using results about the Dickson algebra and by studying the Lannes{Zarati homomorphism. 1
AGENERATORS FOR IDEALS IN THE DICKSON ALGEBRA
"... Abstract. The Dickson Algebra on qvariables is the algebra of invariants of the action of the mod2 general linear group on a polynomial algebra in qvariables. We study the structure of certain ideals in this algebra as a module over the Steenrod Algebra A, and develop methods to determine which e ..."
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Abstract. The Dickson Algebra on qvariables is the algebra of invariants of the action of the mod2 general linear group on a polynomial algebra in qvariables. We study the structure of certain ideals in this algebra as a module over the Steenrod Algebra A, and develop methods to determine which elements are hit by Steenrod operations. This allows us to display a very small set of Agenerators for these ideals and show that the set is minimal in some cases. 1.