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Ball quotients, hyperelliptic varieties, and projective spaces arecharacterized by their Chern classes, as the varieties where the Miyaoka-Yauinequality becomes an equality. Ball quotients, Abelian varieties, andprojective spaces are also characterized topologically: if a complex,projective manifold $X$ is homeomorphic to a variety of this type, then $X$ isitself of this type. In this paper, similar results are established forprojective varieties with klt singularities that are homeomorphic to singularball quotients, quotients of Abelian varieties, or projective spaces.

Miyaoka-Yau inequalities and the topological characterization of certain klt varieties