Higher index theorems and the boundary map in cyclic cohomology

  • Victor Nistor

    6802 USA
Higher index theorems and the boundary map in cyclic cohomology cover
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Abstract

We show that the Chern–Connes character induces a natural transformation from the six term exact sequence in (lower) algebraic -Theory to the periodic cyclic homology exact sequence obtained by Cuntz and Quillen, and we argue that this amounts to a general “higher index theorem.” In order to compute the boundary map of the periodic cyclic cohomology exact sequence, we show that it satisfies properties similar to the properties satisfied by the boundary map of the singular cohomology long exact sequence. As an application, we obtain a new proof of the Connes–Moscovici index theorem for coverings.

Cite this article

Victor Nistor, Higher index theorems and the boundary map in cyclic cohomology. Doc. Math. 2 (1997), pp. 263–295

DOI 10.4171/DM/30