A more general method to classify up to equivariant KK-equivalence II: Computing obstruction classes

TL;DR

This paper develops a general method for computing obstruction classes in equivariant KK-theory, enhancing classification techniques for C*-algebras with group actions by providing explicit invariants and comparisons.

Contribution

It introduces a universal approach to compute obstruction classes in equivariant KK-theory, extending classification results for C*-algebras with group actions.

Findings

Provides Universal Coefficient Theorems for equivariant KK-theory.

Establishes a method to compute obstruction classes explicitly.

Compares different classification invariants and their relationships.

Abstract

We describe Universal Coefficient Theorems for the equivariant Kasparov theory for C*-algebras with an action of the group of integers or over a unique path space, using KK-valued invariants. We compare the resulting classification up to equivariant KK-equivalence with the recent classification theorem involving a K-theoretic invariant together with an obstruction class in a certain Ext^2-group and with the classification by filtrated K-theory. This is based on a general theorem that computes these obstruction classes.