Constructing Menger Manifold C*-Diagonals in Classifiable C*-Algebras

Abstract We initiate a detailed analysis of $C^{\ast }$-diagonals in classifiable }$-algebras, answering natural questions concerning topological properties their spectra and uniqueness questions. Firstly, we construct with connected all stably finite which are unital or projectionless continuous scale. Secondly, for }$-algebras torsion-free $K_0$ trivial $K_1$, further determine the up to homeomorphism. In case, underlying space turns out be Menger curve. is obtained by removing non-locally-separating copy Cantor from Thirdly, show that each our has continuum many pairwise non-conjugate such manifold$C^{\ast }$-diagonals.