GROUPS OF OBSTRUCTIONS TO SURGERY AND SPLITTING FOR A MANIFOLD PAIR

The surgery obstruction groups LP of manifold pairs are studied. An a lgebraic version of these groups for squares of antistructures of a sp ecial form equipped with decorations is considered. The squares of ant istructures in question are natural generalizations of squares of fund amental groups that occur in the splitting problem for a one-sided sub manifold of codimension 1 in the case when the fundamental group of th e submanifold is mapped epimorphically onto the fundamental group of t he manifold. New connections between the groups LP, the Novikov-Wall groups, and the splitting obstruction groups are established.