The Brown-Peterson \([2^ k]\)-series revisited
type: Item
instance of: scholarly article
title: The Brown-Peterson \([2^ k]\)-series revisited
zbMATH Open document ID: 0864.55003
DOI: 10.1016/0022-4049(95)00140-9
author: George Nakos
author: David C. Johnson
published in: Journal of Pure and Applied Algebra
publication date: 1996-11-25T00:00:00Z
review text: The \([2^k]\)-series in Brown-Peterson theory arises from the associated formal group law \(F(X,Y)\) and the inductive definitions, \([1] X=X=F(0,X) =F(X,0)\), \([2] X= F(X,X)\), \([2^k] X=[2]([2^{k-1}]X)\). One can write \([2^k]=\sum_{0\leq s}a_{k,s} X^{s+1}\), \(a_{k,s} \in BP_{2s}\). The coefficients \(a_{k,s}\) generate the relations in the Brown-Peterson homology of \(BZ/2^k\). This paper shows that each coefficient \(a_{k,s}\) has a distinguished shortest monomial which is determined by the dyadic expansion of \(s+1\).
Mathematics Subject Classification ID: 55N22
zbMATH DE Number: 933079
zbMATH Keywords: Brown-Peterson homology
zbMATH Keywords: formal group law
reviewed by: Jonathan Hodgson
MaRDI profile type: Publication
full work available at URL: 0022-4049(95)00140-9
OpenAlex ID: W2031101154
cites work: Q4169919
cites work: A universal formal group and complex cobordism
cites work: On the [p]-series in Brown-Peterson homology
cites work: Two Notes on Notation
cites work: On the \([p^ k]\)-series in Brown-Peterson homology
cites work: Q3667609
description: scientific article; zbMATH DE number 933079