Central Adams operators
type: Item
instance of: scholarly article
title: Central Adams operators
zbMATH Open document ID: 0638.55005
DOI: 10.1007/BF01161924
author: Karlheinz Knapp
author: Michael C. Crabb
published in: Manuscripta Mathematica
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155271
review text: ``From the introduction: ``Let X be a (pointed) finite complex with trivial rational homology. Then, for some, potentially large, integer \(s>0\) there exists a stable map \(B: \Sigma\) \({}^ sX\to X\) which induces an isomorphism \(B^*: KO^*(X)\to KO^*(\Sigma^ sX)\) in (reduced) periodic real K-theory. Such maps were first considered by Adams and Toda. Recent work of Devinatz, Hopkins and Smith shows, as a special first case of a much more general theorem, that B can be chosen to be central in the graded ring \(\pi^*_ s\{X;X\}\) of stable self-maps of X. In this note we reprove this using the elementary methods, based on a solution of the Adams conjecture, that we described in Topology 24, 475- 486 (1985; Zbl 0581.55008). The key idea comes from \textit{M. Hopkins} [Lectures at the Durham Sympos. on Homotopy Theory (1985)].''
Mathematics Subject Classification ID: 55N15
Mathematics Subject Classification ID: 55P42
Mathematics Subject Classification ID: 55R50
Mathematics Subject Classification ID: 55Q10
zbMATH DE Number: 4040830
zbMATH Keywords: Adams periodicity
zbMATH Keywords: Adams map
zbMATH Keywords: graded ring of stable self-maps
zbMATH Keywords: Adams conjecture
reviewed by: Mamoru Mimura
MaRDI profile type: Publication
cites work: On the groups \(J(X)\). IV
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cites work: The Hurewicz Map on Stunted Complex Projective Spaces
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OpenAlex ID: W1997413925
description: scientific article; zbMATH DE number 4040830