Discrete dynamics on noncommutative CW complexes (Q2871998)

A noncommutative CW-complex \(C_{\Sigma}\) is the universal (unital) \(C^*\)-algebra on generators \(h_v\) satisfying the relation \(\sum_{v\in V}h_v=1\), where \(V\) is the set of all vertices of a usual CW-complex \(\Sigma\). For instance, the periodic cyclic homology of \(C_{\Sigma}\) is isomorphic to the \({\mathbb Z}/2\)-graded singular cohomology of the complex \(\Sigma\). The authors study dynamics of diffeomorphisms of \(C_{\Sigma}\) and their relation to the topology of \(C_{\Sigma}\). An example of a dynamical system on the two-dimensional torus \(T^2\) and the corresponding noncommutative CW-complex is considered in greater detail.