The hit problem for \(H^{*}(BU(2); \mathbb F_p)\)
type: Item
instance of: scholarly article
title: The hit problem for \(H^{*}(BU(2); \mathbb F_p)\)
zbMATH Open document ID: 1333.55013
author: David Pengelley
author: Frank Williams
published in: Algebraic \& Geometric Topology
publication date: 2013-06-20T00:00:00Z
review text: The ``hit problem'' for a module over the Steenrod algebra is to identify those elements which are ``hit'', i.e., arise by applying Steenrod operations to lower-degree elements. The remainder give rise to a minimal set of generators for the module. The problem is quite challenging in most cases and has spawned a large and interesting literature since first being raised by Frank Peterson in the 1980s [\textit{F. P. Peterson}, Math. Proc. Camb. Philos. Soc. 105, No. 2, 311--312 (1989; Zbl 0692.55012)]. In this paper the authors solve the problem for the classifying space \(BU(2)\), at odd primes. The results are described in the dual setting of annihilated elements in the homology of \(BU(2)\), and using an action of the Kudo-Araki-May algebra.
Mathematics Subject Classification ID: 55S10
Mathematics Subject Classification ID: 55R40
Mathematics Subject Classification ID: 55R45
Mathematics Subject Classification ID: 16W22
Mathematics Subject Classification ID: 16W50
Mathematics Subject Classification ID: 55S05
Mathematics Subject Classification ID: 57T10
Mathematics Subject Classification ID: 57T25
zbMATH DE Number: 6177496
zbMATH Keywords: Steenrod algebra
zbMATH Keywords: hit problem
zbMATH Keywords: primitive elements
zbMATH Keywords: Kudo-Araki-May algebra
zbMATH Keywords: symmetric invariants
reviewed by: Martin D. Crossley
MaRDI profile type: Publication
full work available at URL: agt.2013.13.2061
OpenAlex ID: W1991785800
cites work: Monomial Bases for 𝐻*(𝐂𝐏^{∞}×𝐂𝐏^{∞}) over 𝒜(𝓅)
cites work: The hit problem for symmetric polynomials over the Steenrod algebra
cites work: Generating H*(BO(3), ${\bb F}_2$) as a module over the Steenrod algebra
cites work: Generators of the cohomology of \(BV_3\)
cites work: A new action of the Kudo-Araki-May algebra on the dual of the symmetric algebras, with applications to the hit problem
cites work: A-generators for certain polynomial algebras
cites work: Rings of symmetric functions as modules over the Steenrod algebra
cites work: Steenrod squares of polynomials and the Peterson conjecture
DOI: 10.2140/AGT.2013.13.2061
description: scientific article; zbMATH DE number 6177496