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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 ..."
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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
Bocksteins and the nilpotent filtration on the cohomology of spaces
, 2007
"... N Kuhn has given several conjectures on the special features satisfied by the singular cohomology of topological spaces with coefficients in a finite prime field, as modules over the Steenrod algebra [4]. The socalled realization conjecture was solved in special cases in [4] and in complete genera ..."
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N Kuhn has given several conjectures on the special features satisfied by the singular cohomology of topological spaces with coefficients in a finite prime field, as modules over the Steenrod algebra [4]. The socalled realization conjecture was solved in special cases in [4] and in complete generality by L Schwartz [9]. The more general strong realization conjecture has been settled at the prime 2, as a consequence of the work of L Schwartz [10] and the subsequent work of FX Dehon and the author [1]. We are here interested in the even more general unbounded strong realization conjecture. We prove that it holds at the prime 2 for the class of spaces whose cohomology has a trivial Bockstein action in high degrees.
Computations in generic representation theory: maps from symmetric powers to composite functors
 Trans. A.M.S
"... Abstract. If Fq is the nite eld of order q and characteristic p, let F(q) be the category whose objects are functors from nite dimensional Fq{vector spaces to Fq{vector spaces, and with morphisms the natural transformations between such functors. Important families of objects in F(q) include the fam ..."
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Abstract. If Fq is the nite eld of order q and characteristic p, let F(q) be the category whose objects are functors from nite dimensional Fq{vector spaces to Fq{vector spaces, and with morphisms the natural transformations between such functors. Important families of objects in F(q) include the families Sn; Sn;n; Sn, and cTn, with c 2 Fq [n], dened by Sn(V) = (V ⊗n)n,Sn(V) = V ⊗n=n, n(V) = nth exterior power of V, S(V) = S(V)=(pth powers), and cTn(V) = c(V ⊗n). Fixing F, we discuss the problem of computing HomF(q)(Sm; F G), for all m, given knowledge of HomF(q)(Sm; G) for all m. When q = p, we get a complete answer for any functor F chosen from the families listed above. Our techniques involve Steenrod algebra technology, and, indeed, our most striking example, when F = Sn, arose in recent work on the homology of iterated loopspaces. 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
 Add to MetaCart
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.
general linear group GLn(F2) and the Poincare
"... and conjectures about the modular representation theory of the ..."
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