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The restrictions on the topology of nonsingular plane projective realalgebraic curves of odd degree, obtained by O. Viro and the author in the paperpublished in the early 90s, are extended to flexible curves lying on an almostcomplex four-dimensional manifold. Some examples of real algebraic surfaces andreal curves on them prove the sharpness of the obtained inequalities.  In addition, it is proved that a compact Lie group smooth action can belifted to a cyclic branched covering space $ \tilde{X} $ over a closedfour-dimensional manifold, and a sufficient condition for $ H_1(\tilde{X})=0 $was found.

Viro-Zvonilov inequalities for flexible curves on an almost complex four-dimensional manifold