Unbounded bivariant $K$-theory and correspondences in noncommutative geometry

Details Unbounded bivariant $K$-theory and correspondences in noncommutative geometry Unbounded bivariant $K$-theory and correspondences in noncommutative geometry

2009-04-28

arxiv.org/abs/0904.4383v4

Mathematics

K-Theory and Homology

64 pages. Rigorous proofs of smoothness preservation are presented. Definition of smooth module modified

Scientific paper

By introducing a notion of smooth connection for unbounded $KK$-cycles, we show that the Kasparov product of such cycles can be defined directly, by an algebraic formula. In order to achieve this it is necessary to develop a framework of smooth algebras and a notion of differentiable $C^{*}$-module. The theory of operator spaces provides the required tools. Finally, the above mentioned $KK$-cycles with connection can be viewed as the morphisms in a category whose objects are spectral triples.

Affiliated with

Also associated with

No associations

Rating

Unbounded bivariant $K$-theory and correspondences in noncommutative geometry does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Unbounded bivariant $K$-theory and correspondences in noncommutative geometry, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Unbounded bivariant $K$-theory and correspondences in noncommutative geometry will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-713024