2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/121817We give elementary proofs of two `folklore' assertions about near-symplectic forms on four-manifolds: that any such form can be modified, by an evolutionary process taking place within a finite set of balls, so as to have a prescribed positive number of zero-circles; and that, on a closed manifold, the number of zero-circles for which the splitting of the normal bundle is trivial has the same parity as 1+b_1+b_2^+.19 pages, 2 figures; to appear in J. Symplectic Geometry. Expository changes in Sections 1 and 4; corrected mistake in the proof of what is now Prop. 1.5Symplectic Geometry57R17; 57R15text