Higher index theorems and the boundary map in cyclic cohomology
Let \(I\subset A\) be a two-sided ideal in a complex algebra. The author shows that the Chern-Connes character induces a natural transformation from the six term exact sequence in (lower) algebraic \(K\)-Theory to the periodic cyclic homology exact sequence obtained by \textit{J. Cuntz} and \textit{D. Quillen} [Invent. Math. 127, No. 1, 67-98 (1997; Zbl 0889.46054)]. The paper also contains further investigations of the properties of the boundary map \(HP^i(I)\to HP^{i+1}(A/I)\) in periodic cyclic cohomology. As an application the author gives a new proof of the Connes-Moscovici index theorem for coverings [see \textit{A. Connes} and \textit{H. Moscovici}, Topology 29, No. 3, 345-388 (1990; Zbl 0759.58047)].
scientific article; zbMATH DE number 1139210