In noncommutative geometry, one is given a triple $(A,D,H)$, where $A$ is a commutative C* algebra, $H$ is a Hilbert space, and $D$ is an operator. There is a somewhat long list of conditions that this data has to satisfy.
There is a finite-dimensional compact manifold $M$ associated with this data. It is equal to the spectrum of $A$.
Question. How are coordinate charts on $M$ constructed? I.e. how is it locally identified with $\mathbb{R}^n$?
