On Iterated Browder–Livesay Invariants

The Browder–Livesay invariants provide obstructions to the realization of elements of Wall groups by normal maps of closed manifolds. A generalization of the iterated Browder–Livesay invariants is proposed and properties of the invariants obtained are described. The generalized definition makes it possible to investigate the relationship between a normal map and its restriction to a submanifold and clarifies the relationship between the Browder–Livesay invariants and the Browder–Quinn groups of obstructions to surgery on filtered manifolds. Several theorems describing a relationship between a normal map and its restriction to a submanifold are proved.