Products and Kunneth theorems in cyclic homology and cohomology theories
Christine E. Hood · Warwick Research Archive Portal (University of Warwick) · 1985
This thesis is concerned with the construction of products in cyclic homology and cohomology, by use of the methods of acyclic models. A theory HC ˉ͙ (A) which is dual to cyclic cohomology HC *(A) over its natural coefficients is introduced, and products are defined HC ˉ͙ (A) and HC * (A). The product then induced on cyclic homology HC ͙(A) is shown to agree with that defined by Loday and Quillen. By using HC ˉ͙ (A), it is possible to construct a multiplicative chern character ch : K ᵢ (A) → HC ˉᵢ-2α (A). Kunneth theorems in the various theories are proved, and some examples are considered.