Operator Algebra Seminar

Abstract: In 1970, G. Segal gave one of the earliest treatments of Fredholm complexes whose index takes values in an abstract K-group. In this talk, we introduce the noncommutative counterpart of this theory: Fredholm complexes of Hilbert C*-modules. Our goal is to define the Fredholm property of complexes of Hilbert C*-modules, and to show how to associate a Fredholm index that takes values in the K-group of the C*-algebra. This talk is based on my master’s thesis under the supervision of Koen van den Dungen.