The product on topological Hochschild homology of the integers with \(\mod 4\) coefficients
type: Item
instance of: scholarly article
title: The product on topological Hochschild homology of the integers with \(\mod 4\) coefficients
zbMATH Open document ID: 0927.55010
DOI: 10.1016/S0022-4049(97)00154-0
author: John Rognes
published in: Journal of Pure and Applied Algebra
publication date: 1999-12-08T00:00:00Z
review text: \textit{Marcel Bökstedt} (unpublished) defined topological Hochschild homology (THH) and calculated the homotopy groups of topological Hochschild homology of the integers. Topological Hochschild homology is equivalent to stable \(K\)-theory, and the relation to \(K\)-theory was the main motivation for studying THH. In this paper the author studies the mod \(2\) and mod \(4\) homotopy of topological Hochschild homology of the integers, and identifies the multiplicative structure. The product with mod \(4\) coefficients is important because it is equivariant with respect to the cyclic structure, and gives a module structure on \(\text{THH}(\mathbf Z)\) with \(\text{mod } 2\) coefficients. The ultimate aim of these calculations is to determine the topological cyclic homology of the integers with \(\text{mod } 2\) coefficients, and hence the algebraic \(K\)-theory of the 2-adic integers with \(\text{mod }2\) coefficients. This is achieved in a later paper [ibid. 134, 219-286 (1999)].
Mathematics Subject Classification ID: 55N45
Mathematics Subject Classification ID: 16E40
Mathematics Subject Classification ID: 55N35
Mathematics Subject Classification ID: 55N15
Mathematics Subject Classification ID: 19D55
Mathematics Subject Classification ID: 55P42
zbMATH DE Number: 1308295
zbMATH Keywords: topological Hochschild homology
zbMATH Keywords: Moore spectra
zbMATH Keywords: stable K-theory
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1308295