Assembly maps and realization of splitting obstructions

Surgery on pairs of closed manifolds

“…A result that is similar to Theorem 3 and Proposition 4 also takes place. It follows easily from the relations between the surgery spectral sequence and the Browder-Quinn surgery obstruction groups (see [14], [10], and [22]). This forbidden invariant is given by the composition…”

“…. ⊂ X 2 ⊂ X 1 ⊂ X 0 = X of a closed connected topological n-dimensional manifold X by locally flat closed submanifolds, the Browder-Quinn surgery obstruction groups are defined (see [6], [10], [22], and [32]). We have natural forgetful maps…”

“…Some results about the realization of the splitting obstructions for specified classes of groups were obtained in [1], [10], and [17].…”

“…We use definitions and results in surgery theory from [2], [8], [9], [12], [19], [24], [25], and [29], and many applications of them to surgery on stratified manifolds (see [4], [6], [10], [17], [22], [23], and [32]). In Section 2 we prove several general technical results, and then use them to study the closed manifold surgery problem for LP * -groups in the case of a Browder-Livesay pair with an abelian 2-group of the ambient manifold.…”