Finiteness properties of certain topological graph algebras

putri salsabilla;

Let E = (E0,E1, r, s) be a topological graph with no sinks such that E0 and E1 are compact. We show that when C∗(E) is finite, there is a natural isomorphism C∗(E)∼=C(E∞) Z, whereE∞ is the infinite path space of E and the action is given by the backwards shift on E∞. Combining this with a result of Pimsner, we show the properties of being approximately finitedimensional-embeddable, quasidiagonal, stably finite, and finite are equivalent for C∗(E) and can be characterized by a natural ‘combinatorial’ condition on E.