This is an announcement for the paper “On the classification of positions and of complex structures in Banach spaces” by Razvan Anisca<https://arxiv.org/find/math/1/au:+Anisca_R/0/1/0/all/0/1>, Valentin Ferenczi<https://arxiv.org/find/math/1/au:+Ferenczi_V/0/1/0/all/0/1>, Yolanda Moreno<https://arxiv.org/find/math/1/au:+Moreno_Y/0/1/0/all/0/1>. Abstract: A topological setting is defined to study the complexities of the relation of equivalence of embeddings (or "position") of a Banach space into another and of the relation of isomorphism of complex structures on a real Banach space. The following results are obtained: a) if $X$ is not uniformly finitely extensible, then there exists a space $Y$ for which the relation of position of $Y$ inside $X$ reduces the relation $E_0$ and therefore is not smooth; b) the relation of position of $\ell_p$ inside $\ell_p$, or inside $L_p$, $p\neq 2$, reduces the relation $E_1$ and therefore is not reducible to an orbit relation induced by the action of a Polish group; c) the relation of position of a space inside another can attain the maximum complexity $E_{max}$; d) there exists a subspace of $L_p$, $1\leq p<2$, on which isomorphism between complex structures reduces $E_1$ and therefore is not reducible to an orbit relation induced by the action of a Polish group. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1701.04263