Bolotov D. Topology and macroscopic geometry of Riemannian manifolds

The thesis is devoted to studying topological, homotopic and macroscopic invariants of Riemannian manifolds, their foliations and mappings. Gromov's problems on macroscopic dimension of universal coverings of closed Riemannian manifolds, in particular, SPC-manifolds is solved in part. G. Stuck problem on existence of codimension one nonnegative curvature foliation on spheres is solved. Topological characterization of flat foliations is done. The method for constructing of saddle foliations on three dimensional manifolds, in particular, on three dimensional sphere was presented. Finiteness of homotopical classes of distributions tangent to the foliations on two dimensional torus, such that curvature of leaves are bounded above by a constant is proved. New Hilbert theorem about non-immersibility of Lobachevski space to Euclidean space is proved. The question of Cohen and Lusk about the partial gluing of an orbit under a map of a free Zp-space to Euclidean space is answered in part. The problem of Yu. Zelinsky about the existence of 2-convex embeddings of two-dimensional spheres to the four-dimensional Euclidean space is solved in the case of smooth embeddings.