I'm sorry, what is that you denote by $cof$?

Thank you very much for your answer. Unfortunately, I am not that familiar with generalized homology theories. I'll definitely try learn more about them. Meanwhile... Could you please be so kind as to expand you answer a bit? add some comments?

But the level $z = \text{const}$ is just a point and that's why it's isotropic. So, I mean $\left\{f_1, f_2\right\}|_{\text{level F}} = 0$. This effect exists only in dimension 4.

Of course, they should be independent.

Yea? So, it is not true that for every function $F = f_1 + i f_2$ the Poisson bracket $\left\{ f_1, f_2 \right\} = 0$ if and only if $F$ is holomorphic?

Ok, thanks. It looks like that I should reformulate my question: which symplectic submanifolds can be realized in $(\mathbb{R}^4(p_1, q_1, p_2, q_2), \omega^2)$? Here $\omega = \text{d}\,\boldsymbol{p} \wedge \text{d}\,\boldsymbol{q}$.

I'm sorry, but I don't understand. The level of holomorphic function in $\mathbb{C}^2$ is lagrangian, not symplectic.