Victor Nistor

摘要

We show that the Chern--Connes character induces a naturaltransformation from the six term exact sequence in (lower) algebraic$K$--Theory to the periodic cyclic homology exact sequence obtained byCuntz and Quillen, and we argue that this amounts to a general``higher index theorem.'' In order to compute the boundary map of theperiodic cyclic cohomology exact sequence, we show that it satisfiesproperties similar to the properties satisfied by the boundary map ofthe singular cohomology long exact sequence. As an application, weobtain a new proof of the Connes--Moscovici index theorem forcoverings.