Bivariant cyclic cohomology and Connes' bilinear pairings in Non-commutative motives

Details Bivariant cyclic cohomology and Connes' bilinear pairings in Non-commutative motives Bivariant cyclic cohomology and Connes' bilinear pairings in Non-commutative motives

2010-05-13

arxiv.org/abs/1005.2336v2

Mathematics

K-Theory and Homology

Exposition improved. 10 pages

Scientific paper

In this article we further the study of non-commutative motives. We prove that bivariant cyclic cohomology (and its variants) becomes representable in the category of non-commutative motives. Furthermore, Connes' bilinear pairings correspond to the composition operation. As an application, we obtain a simple model, given in terms of infinite matrices, for the (de)suspension of these bivariant cohomology theories.

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