Article ID Journal Published Year Pages File Type
8896584 Journal of Functional Analysis 2018 52 Pages PDF
Abstract
We develop a generalization of quantitative K-theory, which we call controlled K-theory. It is powerful enough to study the K-theory of crossed product of C⁎-algebras by action of étale groupoids and discrete quantum groups. In this article, we will use it to study groupoids crossed products. We define controlled assembly maps, which factorize the Baum-Connes assembly maps, and define the controlled Baum-Connes conjecture. We relate the controlled conjecture for groupoids to the classical conjecture, and to the coarse Baum-Connes conjecture. This allows to give applications to Coarse Geometry. In particular, we can prove that the maximal version of the controlled coarse Baum-Connes conjecture is satisfied for a coarse space which admits a fibred coarse embedding, which is a stronger version of a result of M. Finn-Sell.
Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
Authors
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