Cyclic homology of formal spaces
type: Item
instance of: scholarly article
title: Cyclic homology of formal spaces
zbMATH Open document ID: 0802.55011
DOI: 10.1016/0022-4049(94)90150-3
author: Micheline Vigué-Poirrier
published in: Journal of Pure and Applied Algebra
publication date: 1994-11-10T00:00:00Z
review text: A 1-connected topological space, \(X\), is called \(\mathbb{Q}\)-formal iff there exists a differential graded algebra \((A,d_ A)\) and quasi-isomorphisms \(C^*(X,Q)\leftarrow (A, d_ A) \to H^* (X;Q)\). The author proves that the Connes operator \(S\) is zero on the reduced cyclic homology of \(X\). This implies that the cohomology of the free loop space on \(X\) can be written as a direct sum \(H^* (BS^ 1)\oplus T^*\) where \(T^*\) is a trivial \(H^* (BS^ 1)\)-module. Explicit calculations have been done by \textit{A. E. Tralle} [Czech. Math. J. 43, No. 4, 615-634 (1993; see the review above)].
Mathematics Subject Classification ID: 55P62
Mathematics Subject Classification ID: 55N91
zbMATH DE Number: 500580
zbMATH Keywords: formal space
zbMATH Keywords: Connes operator
zbMATH Keywords: cyclic homology
zbMATH Keywords: free loop space
reviewed by: Jean-Claude Thomas
MaRDI profile type: Publication
full work available at URL: 0022-4049(94)90150-3
OpenAlex ID: W2006763635
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description: scientific article; zbMATH DE number 500580