Self maps of spectra, a theorem of J. Smith, and Margolis' killing construction
type: Item
instance of: scholarly article
title: Self maps of spectra, a theorem of J. Smith, and Margolis' killing construction
zbMATH Open document ID: 0792.55005
DOI: 10.1007/BF02571725
author: Hal Sadofsky
author: John H. Palmieri
published in: Mathematische Zeitschrift
publication date: 1994-08-07T00:00:00Z
full work available at URL: https://eudml.org/doc/174623
review text: We prove that certain spectra have self-maps easily described in terms of \(\text{Ext}^{**}_ A(\cdot,\cdot)\). We apply this to prove Jeff Smith's theorem that for each \(n\), there is a finite spectrum admitting a \(v_ n\)-map. other applications are Margolis' killing construction for spectra and a spectral sequence for computing the homotopy of some \(v_ n\)-periodic telescopes.
Mathematics Subject Classification ID: 55P42
Mathematics Subject Classification ID: 55T99
zbMATH DE Number: 567413
zbMATH Keywords: spectra
zbMATH Keywords: \(v_ n\)-map
zbMATH Keywords: spectral sequence
zbMATH Keywords: telescopes
MaRDI profile type: Publication
cites work: Modules over the Steenrod algebra
cites work: A vanishing theorem in homological algebra
cites work: The localization of spectra with respect to homology
cites work: Nilpotence and stable homotopy theory. I
cites work: Q3805461
cites work: Nilpotence and stable homotopy theory. II
cites work: The order of the image of the 𝐽-homomorphism
cites work: The image of J in the EHP sequence
cites work: \(\nu_n\) telescopes and the Adams spectral sequence
cites work: Q3345437
cites work: Eilenberg-Mac Lane Spectra
cites work: On relations between Adams spectral sequences, with an application to the stable homotopy of a Moore space
cites work: Vanishing lines for modules over the Steenrod algebra
cites work: Finite complexes with A(n)-free cohomology
cites work: On the Composition Pairing of Adams Spectral Sequences
cites work: Self-maps of modules over the Steenrod algebra
cites work: The v 1 -Periodic Homotopy Groups of an Unstable Sphere at Odd Primes
description: scientific article; zbMATH DE number 567413