Trieste, August 26-28 2014

K-homology and graph algebras

Graph reconstruction and noncommutative geometry

Given a finite graph, we consider the crossed product algebra of the action of its fundamental group on the boundary of its universal covering tree. As an operator algebra, this contains only topological information about the graph, but when enhanced by a suitable one-parameter group of automorphisms, one can reconstruct any multigraph with minimal degree three. Joint work with Matilde Marcolli.