A. D. Alexandrov's length manifolds with one-laterally bounded curvature

The paper is devoted to discovering relations between inner metrics of manifolds with sectional curvature bounded from above (from below) by some constant and topological (simplicial, piecewise-linear, or smooth) structures on such manifolds. Examples of Alexandrov spaces with one-laterally bounded curvature having exotic properties are given. Bibl. 5 titles.