Topological graphs and singly generated dynamical systems

Abstract

In this paper, we introduce the notion of a dual topological graph of a given topological graph, and show that it defines a C*-algebra isomorphic to the C*-algebra of the given one. Repeating to take a dual, and taking a projective limit, we get a singly generated dynamical system with which the associate C*-algebra is isomorphic to the C*-algebra of the given topological graph. This shows that a C*-algebra of an arbitrary topoloical graph has a groupoid model. Similar investigation are done for relative topoloical graphs and partially defined topoloical graphs which are introduced in this paper.