Nonunital spectral triples and metric completeness in unbounded KK-theory
Operator Algebras
2016-10-24 v2 K-Theory and Homology
Metric Geometry
Abstract
By considering the general properties of approximate units in differentiable algebras, we are able to present a unified approach to characterising completeness of spectral metric spaces, existence of connections on modules, and the lifting of Kasparov products to the unbounded category. In particular, by strengthening Kasparov's technical theorem, we show that given any two composable KK-classes, we can find unbounded representatives whose product can be constructed to yield an unbounded representative of the Kasparov product.
Keywords
Cite
@article{arxiv.1502.04520,
title = {Nonunital spectral triples and metric completeness in unbounded KK-theory},
author = {Bram Mesland and Adam Rennie},
journal= {arXiv preprint arXiv:1502.04520},
year = {2016}
}
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65 pages