Groupoids decomposition, propagation and K-theory

TL;DR

This paper refines the groupoid coarse decomposition technique to improve K-theory calculations for groupoid crossed products, leveraging controlled operator K-theory to advance understanding in this area.

Contribution

It introduces a streamlined approach to groupoid decomposition for K-theory, enhancing computational methods originally developed by Yu for the Novikov conjecture.

Findings

Improved method for K-theory computations of groupoid crossed products.

Application of controlled operator K-theory to groupoid decomposition.

Enhanced understanding of the relationship between groupoid structure and K-theory.

Abstract

In this paper, we streamline the technique of groupoids coarse decomposition for purpose of K-theory computations of groupoids crossed products. This technique was first introduced by Guoliang Yu in his proof of Novikov conjecture for groups with finite asymptotic dimension. The main tool we use for these computations is controlled operator K-theory.