Existence of the Greek letter elements in the stable homotopy groups of \(E(n)_ *\)-localized spheres
type: Item
instance of: scholarly article
title: Existence of the Greek letter elements in the stable homotopy groups of \(E(n)_ *\)-localized spheres
zbMATH Open document ID: 0824.55002
author: Katsumi Shimomura
author: Masaaki Yokotani
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1994-09-27T00:00:00Z
review text: Let \(E_ 2^{*,*}\) denote the \(E_ 2\)-term of the Adams-Novikov spectral sequence converging to the homotopy groups of \(X\). This paper shows how to define Greek letter elements in \(E_ 2^{*,*} (L_ n S^ 0)\) where \(L_ n\) denotes the Bousfield localization with respect to the spectrum \(\nu_ n^{-1} (BP)\). The elements are shown to be permanent cycles corresponding to the Greek letter elements in \(E_ 2^{*,*} (S^ 0)\).
Mathematics Subject Classification ID: 55N22
Mathematics Subject Classification ID: 55Q45
Mathematics Subject Classification ID: 55T15
Mathematics Subject Classification ID: 55N20
Mathematics Subject Classification ID: 55P42
Mathematics Subject Classification ID: 55Q10
Mathematics Subject Classification ID: 57R77
zbMATH DE Number: 621970
zbMATH Keywords: \(E_ 2\)-term of the Adams-Novikov spectral sequence
zbMATH Keywords: Brown-Peterson spectrum
zbMATH Keywords: Greek letter elements
zbMATH Keywords: Bousfield localization
reviewed by: Jonathan Hodgson
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195166279
OpenAlex ID: W1976506155
cites work: Q4067782
cites work: On Bordism Theory of Manifolds with Singularities.
cites work: A spectrum whose \(Z_ p\) cohomology is the algebra of reduced \(p\)-th powers
cites work: Relations between several Adams spectral sequences
cites work: Nilpotence and stable homotopy theory. II
cites work: Torsion in Brown-Peterson homology and Hurewicz homomorphisms
cites work: Invariant regular ideals in Brown-Peterson homology
cites work: Homological Properties of Comodules Over MU ∗ (MU) and BP ∗ (BP)
cites work: Periodic phenomena in the Adams-Novikov spectral sequence
cites work: A cellular construction of BP and other irreducible spectra
cites work: Localization with Respect to Certain Periodic Homology Theories
cites work: Q3747338
cites work: BP-Hopf module spectrum and \(BP_ *\)-Adams spectral sequence
cites work: On spectra realizing exterior parts of the Steenrod algebra
cites work: On products in a family of cohomology theories associated to the invariant prime ideals of \(\pi_*(BP)\)
DOI: 10.2977/PRIMS/1195166279
description: scientific article; zbMATH DE number 621970