Cyclic homology of formal spaces
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)].
scientific article; zbMATH DE number 500580