respectively. Suppose that $M_1$ and $M_2$ intersect transversally at zero, [**]{}, $v_1, w_1, v_2, w_2$ is the basis of $\rr^4$. We say that they intersect positively if this basis gives the same orientation of $\rr ^4$ as the standard one.

Let $(X,\omega )$ be a manifold with nowhere degenerate exterior $2$-form $\omega $.

Definition 1.4.1. [*An immersion $u:S\to X$ of a real surface $S$ into $X$ is called $\omega $-positive if $u^*\omega $ never vanishes.* ]{}

If $\omega $ is symplectic we call such immersions [*symplectic*]{}.

Definition 1.4.2. [*An almost-complex structure $J$ is said to be tamed by an exterior $2$-form $\omega $ if $\omega (u,Ju)>0$ for any nonzero $u\in TX$*]{}.

In the following lemma we suppose for simplicity of proof that $\dim_{\rr }X
=4$.

Lemma 1.4.2.

*Let $M$ be a $\omega $-positive compact surface immersed into $(X,\omega )$ with only double positive local self-intersections, and let $U_1\subset \subset U$ be neighborhoods of $M$. Then for any given $\omega $-tamed a.-c. structure $J$ there exists a smooth family $\{ J_t\} _{t\in [0, 1]} $ of almost-complex structures on $X$ such that:*

a\) $J_0$ is the given structure $J$ on $X$;

b\) for each $t\in [0, 1]$ the set $\{ x\in 