Cubical, categorical & continuous: comparing cohomologies coming from k-graphs

Jianchao Wu  (Penn State University)

13:00 pm to 14:00 pm, December 26th, 2016   Science Building A1510

Abstract:

Higher rank graphs, also called $k$-graphs, are higher dimensional generalizations of ordinary directed graphs. They provide a rich source of interesting nuclear $C^\ast$-algebras whose properties are often intricately related to the underlying $k$-graph. Adding to this richness is the possibility of twisting a k-graph algebra by a 2-cocycle of the k-graph. In this sense, twisted k-graph algebras are a generalization of noncommutative tori. This motivated the systematical study of the cohomology of k-graphs, which comes in two flavors: cubical and categorical. Also related is the continuous cohomology of the associated groupoid. I will talk about my recent joint work with Elizabeth Gillaspy on revealing the close relations between these cohomologies and their applications to the twisted $k$-graph $C^\ast$-algebras.