Quantitative K-theory and the K{\"u}nneth formula for operator algebras

TL;DR

This paper develops an algorithm using quantitative operator K-theory to compute K-theory for filtered C*-algebras with asymptotic finite nuclear decomposition and proves the K{"u}nneth formula for this class.

Contribution

It introduces a new algorithm for K-theory computation and establishes the K{"u}nneth formula for a specific class of C*-algebras using a quantitative Mayer-Vietoris sequence.

Findings

Algorithm for K-theory computation for filtered C*-algebras

Proof of K{"u}nneth formula for this class of algebras

Development of a quantitative Mayer-Vietoris sequence

Abstract

In this paper, we apply quantitative operator K-theory to develop an algorithm for computing K-theory for the class of filtered C *-algebras with asymptotic finite nuclear decomposition. As a consequence, we prove the K{\"u}nneth formula for C *-algebras in this class. Our main technical tool is a quantitative Mayer-Vietoris sequence for K-theory of filtered C *-algebras.