Hermitian \(K\)-theory of \(A_{\infty{}}\) rings. Homotopy invariance and the hyperbolic map
type: Item
instance of: scholarly article
title: Hermitian \(K\)-theory of \(A_{\infty{}}\) rings. Homotopy invariance and the hyperbolic map
zbMATH Open document ID: 0768.55010
DOI: 10.1007/BF00997381
author: Zbigniew Fiedorowicz
author: Roland Schwänzl
author: Rainer Vogt
published in: \(K\)-Theory
publication date: 1993-05-16T00:00:00Z
review text: This paper is concerned with Hermitian \(A_ \infty\) rings, as constructed by the authors in [ibid. 519-558 (1992; see the preceding review)]. Let \(X\) be a Hermitian \(A_ \infty\) ring; this means that \(X\) is a homotopy-theoretic version of a ring with involution. The authors construct Hermitian \(K\)-theory spaces \(_ 1L(X)\) and \(_{-1}L(X)\), show that they are infinite loop spaces, and give homotopy invariance results. They also relate them to spaces of matrices, to the Hermitian \(K\)-theory of discrete rings, and to the algebraic \(K\)-theory \(K(X)\) of \(X\). In particular they construct a hyperbolic map from \(K(X)\) to \(_{\pm 1}L(X)\).
Mathematics Subject Classification ID: 55P47
Mathematics Subject Classification ID: 19G38
zbMATH DE Number: 166868
zbMATH Keywords: Hermitian \(A_ \infty\) rings
zbMATH Keywords: homotopy-theoretic version of a ring with involution
zbMATH Keywords: Hermitian \(K\)-theory spaces
zbMATH Keywords: Hermitian \(K\)-theory
zbMATH Keywords: algebraic \(K\)-theory
zbMATH Keywords: infinite loop spaces
reviewed by: Richard John Steiner
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 166868