Homotopical Stable Ranks for Certain C*-algebras

TL;DR

This paper investigates the stable ranks of C*-algebras, providing estimates for pullbacks and tensor products, and applies these findings to specific classes including commutative and non-commutative CW-complexes.

Contribution

It introduces new methods to estimate homotopical stable ranks for complex C*-algebra constructions and computes these ranks for particular classes.

Findings

Estimated stable ranks for pullbacks of C*-algebras

Derived stable ranks for tensor products with commutative C*-algebras

Determined stable ranks for certain commutative and non-commutative CW-complexes

Abstract

We study the general and connected stable ranks for C*-algebras. We estimate these ranks for pullbacks of C*-algebras, and for tensor products by commutative C*-algebras. Finally, we apply these results to determine these ranks for certain commutative C*-algebras, and non-commutative CW-complexes.