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

2025/05/07 by Arturo Jaime, Jaime, Arturo
Mathematics · #19K35 #Advanced Topology and Set Theory #FOS: Mathematics #K-Theory and Homology (math.KT) #Mathematical Dynamics and Fractals #Mathematical and Theoretical Analysis #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2505.04117

openalex publication_date 2025/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• On the topology of the Kasparov groups and its applications
• The Fine Structure of the Kasparov Groups II: topologizing the UCT

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• Controlled KK-theory, and a Milnor exact sequence
• Controlled K-theory I: Basic theory
• Aspects of equivariant KK-theory in its generators and relations picture
• Topological K-homology for non-proper actions and assembly maps
• Algebraic K-theory and trace invariants