3-manifolds and 4-dimensional surgery

الأصل · EN

Let X be a connected compact 3-manifold with non-empty boundary. Consider the boundary M of X× D². M is a 4-dimensional closed manifold and has the same fundamental group as X. Various examples of X are known for which a certain assembly map A:H₄(X;L)→ L₄(π₁(X)) is injective. For such an X and any CW-spine B of X, there is a UV¹-map p:M→ B. For any ε>0, if the surgery obstruction for a TOP normal map (f,b):N→ M vanishes, we can perform surgery on f to change it into a p⁻¹(ε)-controlled homotopy equivalence.