UNBOUNDED BIVARIANT K-THEORY AND CORRESPONDENCES IN NONCOMMUTATIVE GEOMETRY

By B. Mesland. 2009

99 citations recorded by the source corpus.

By adapting the algebraic notion of universal connection to the setting of 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.

View Paper: https://www.semanticscholar.org/paper/e9868fcda8ab58184169178e8740d8882707c390

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1. A. Rennie
2. B. Mesland
3. David Pask
4. Alan L. Carey

Citations in the corpus

• Nonunital spectral triples and metric completeness in unbounded KK-theory (2015, methodology): “The following theorem generalises the observations in the appendix to [41].”