On real homotopy properties of complete intersections

The real homotopy type of complete intersections in $\mathbf CP^N$ is studied. It is proved that these manifolds are intrinsically formal in the sense of Stashev and Gal'perin. The Poincaré series of the loop space on complete intersections is computed, and thus the validity of the Serre conjecture on the rationality for such complexes is established. As a corollary, a formula for the rational homotopy groups of a complete intersection is obtained.
Bibliography: 12 titles.