Speaker: Nanami Hashimoto (Keio University)

Title: Equivalence of categories of KK-theory or E-theory for C*-algebras over topological spaces by reflection functors

Time/Date: July 7 (Tue), 2026, 4:45-6:15pm

Room: 126 Math. Sci. Building

Abstract: In this talk, I will introduce reflection functors, inspired by the classical BGP-reflection functors in the representation theory of quivers, between the categories of Kirchberg's ideal-related KK-theory for various pairs of finite T_0-spaces. These functors induce equivalences between the corresponding bootstrap categories. As a consequence, the bootstrap category for a finite T_0-space whose Hasse diagram is an orientation of a tree depends only on the underlying tree. I will also establish analogous results for Dadarlat and Meyer's ideal-related E-theory. Finally, I will explain how reflection functors can be applied to show that filtrated K-theory satisfies the universal coefficient theorem for C*-algebras over finite T_0-spaces whose Hasse diagrams are orientations of Dynkin diagrams of type A.