Semiprojectivity and Graph Algebras

The theory of graph C*-algebras has played an important role in the understanding of semiprojectivity of C*-algebras, most notably in the work of Spielberg. More recently, work of Katsura and the advisor in has resolved the question of when unital graph algebras are semiprojective, relating this issue to the proper infiniteness of certain projections. The core of this paper is a thorough account of this work, including the characterization of proper infiniteness of relevant projections, followed by an account of Spielberg's methods.