2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/98864We prove that the minimal Euler characteristic of a closed symplectic four-manifold with given fundamental group is often much larger than the minimal Euler characteristic of almost complex closed four-manifolds with the same fundamental group. In fact, the difference between the two is arbitrarily large for certain groups.cosmetic changes only; final version, to appear in Proc. Amer. Math. SocGeometric TopologySymplectic Geometry57M07;57R17;57R57text