FACTOR SYSTEMS AS A COMPUTATIONAL FRAMEWORK FOR NONCOMMUTATIVE PRINCIPAL BUNDLES

Free actions in the sense of Ellwood provide a natural framework for C*-algebraic noncommutative principal bundles, which are becoming increasingly prevalent in various applications to noncommutative geometry and mathematical physics. One of the key features of free actions of compact quantum groups is their associated factor systems, which make them accessible to classification, K-theoretic considerations, and computations in general. In this talk, we will give an introduction to the theory of factor systems for free actions of compact quantum groups, followed by a discussion of various applications.