Topology of KK-theory via inverse limits of discrete abelian groups

TL;DR

This paper investigates the topological structure of KK-theory groups for pro-countable abelian groups, using inverse limits and the Milnor exact sequence to analyze properties like Mittag-Leffler and stability conditions.

Contribution

It provides a new characterization of KK-theory topological groups through inverse limits and exact sequences, linking algebraic and topological properties.

Findings

Describes topological properties of KK(A,B) groups

Relates Mittag-Leffler conditions to KK-theory stability

Uses Milnor exact sequence to analyze inverse systems

Abstract

This paper seeks to characterize some topological properties of pro-countable abelian topological groups. Using the Milnor exact sequence given by the controlled picture of $KK$-theory by Willett and Yu, we describe topological properties of the topological group $KK(A,B)$ with respect to the satisfaction of Mittag-Leffler and stability conditions of certain inverse systems.