On May spectral sequences
type: Item
instance of: scholarly article
title: On May spectral sequences
zbMATH Open document ID: 0897.55014
author: Mizuho Hikida
published in: Journal of Mathematics of Kyoto University
publication date: 1998-10-11T00:00:00Z
review text: Let \(\lambda:E\rightarrow F\) be a map of ring spectra. In an earlier paper [Hiroshima Math. J. 19, No. 1, 37-76 (1989; Zbl 0724.55015)] the author described a method for calculating the differentials in the Adams spectral sequence based on \(E\) using those of the May spectral sequence based on \(F\), extending results first proved by \textit{Haynes R. Miller} [J. Pure Appl. Algebra 20, 287-312 (1981; Zbl 0459.55012)]. The current paper is devoted to relating the May spectral sequence to the algebraic Novikov spectral sequence based on \(E\), giving methods for computing the latter, and giving conditions under which these two are isomorphic. Again this extends earlier results of Miller's. Applications of these results to construct elements in the stable homotopy groups of spheres are promised in a future paper.
Mathematics Subject Classification ID: 55T15
Mathematics Subject Classification ID: 55P42
zbMATH DE Number: 1140500
zbMATH Keywords: map of ring spectra
zbMATH Keywords: algebraic Novikov spectral sequence
reviewed by: Keith Johnson
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250518403
OpenAlex ID: W1495394018
DOI: 10.1215/KJM/1250518403
description: scientific article; zbMATH DE number 1140500