2023/06/23 by José R. Carrión, Carrión, José R., Christopher Schafhauser +1
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.2306.13757
openalex publication_date 2023/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For separable C^*-algebras A and B, we define a topology on the set [[A, B]] consisting of homotopy classes of asymptotic morphisms from A to B. This gives an enrichment of the Connes--Higson asymptotic category over topological spaces. We show that the Hausdorffization of this category is equivalent to the shape category of Dadarlat. As an application, we obtain a topology on the E-theory group E(A, B) with properties analogous to those of the topology on KK(A, B). The Hausdorffized E-theory group EL(A, B) = E(A, B) / \0\ is also introduced and studied. We obtain a continuity result for the functor EL( ⋅ ,B), which implies a new continuity result for the functor KL( ⋅ ,B).