Finite Cyclic Fundamental Groups and Exotic Universal Covers from the Cartwright--Steger Surface

We use a particular nodal curve on the Cartwright-Steger surface to construct minimal symplectic four-manifolds with arbitrary nontrivial finite cyclic fundamental group and fixed topological invariants $(e,\sigma ,{\chi }_h,c_1^2)=(43,1,11,89)$. Using these symplectic four-manifolds as building blocks, we construct a symplectic 4-manifold that is homeomorphic to $(22m-1){\mathbb{C}\mathbb{P}}^2\mathrm{\#}(21m-1){\overline{\mathbb{C}\mathbb{P}}}^2$ for any integer $m\ge 2$.