The product on topological Hochschild homology of the integers with \(\mod 4\) coefficients
\textit{Marcel Bökstedt} (unpublished) defined topological Hochschild homology (THH) and calculated the homotopy groups of topological Hochschild homology of the integers.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)].
scientific article; zbMATH DE number 1308295