Projective splitting obstruction groups for one-sided submanifolds

A geometric diagram of groups, which consists of groups equipped with geome tric antistructures, is a natural generalization of the square of fundament al groups arising in the splitting problem for a one-sided submanifold. In the present paper the groups LS* and LP* of such diagrams are defined and t he properties of these groups are described. Methods for the computation of LS*p, LP*p-groups and natural maps in diagrams of exact sequences are deve loped in the case of a geometric diagram of finite 2-groups.