2020/08/31 by Martino Lupini, Lupini, Martino
Mathematics · Physics and Astronomy · #19K33 #46L80 (Secondary) #54H05 (Primary) 46M20 #Advanced Operator Algebra Research #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Logic (math.LO) #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.2008.13344
openalex publication_date 2020/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we show that the K-homology groups of a separable C*-algebra can be enriched with additional descriptive set-theoretic information, and regarded as definable groups. Using a definable version of the Universal Coefficient Theorem, we prove that the corresponding definable K-homology is a finer invariant than the purely algebraic one, even when restricted to the class of UHF C*-algebras, or to the class of unital commutative C*-algebras whose spectrum is a 1-dimensional connected subspace of ℝ3.