The second real Johnson-Wilson theory and nonimmersions of \(RP^n\)
type: Item
instance of: scholarly article
title: The second real Johnson-Wilson theory and nonimmersions of \(RP^n\)
zbMATH Open document ID: 1160.55002
author: Nitu Kitchloo
author: W. Stephen Wilson
published in: Homology, Homotopy and Applications
publication date: 2009-03-10T00:00:00Z
full work available at URL: http://intlpress.com/hha/v10/n3/
review text: The \(m\)th real Johnson--Wilson spectrum \(ER(m)\) is a \(2^{m+2}(2^m-1)\)-periodic spectrum constructed from the \(2(2^m-1)\)-periodic spectrum \(E(m)\); for example \(ER(1)\) and \(E(1)\) are orthogonal and unitary \(K\)-theory localised at \(2\). The authors set up a Bockstein spectral sequence to compute \(ER(m)^*(X)\) from \(E(m)^*(X)\), and they compute \(ER(m)^*(X)\) when \(X\) is an infinite-dimensional real projective space. They then compute \(ER(2)^*(X)\), where \(X\) is a finite-dimensional real projective space \(\mathbb RP^n\). From these computations they obtain new nonimmersion theorems for \(\mathbb RP^n\). The lowest-dimensional new result is for \(\mathbb{R} P^{48}\).
reviewed by: Richard John Steiner
Mathematics Subject Classification ID: 55N22
Mathematics Subject Classification ID: 55N91
Mathematics Subject Classification ID: 55T25
Mathematics Subject Classification ID: 57R42
zbMATH DE Number: 5527623
zbMATH Keywords: Johnson-Wilson theory
zbMATH Keywords: real projective space
zbMATH Keywords: immersion
MaRDI profile type: Publication
OpenAlex ID: W2156282630
DOI: 10.4310/HHA.2008.V10.N3.A11
description: scientific article; zbMATH DE number 5527623