3-manifolds and 4-dimensional surgery

2006/10/25 by Masayuki Yamasaki, Yamasaki, Masayuki
Mathematics · #57R67 #Advanced Operator Algebra Research #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.math/0610741

openalex publication_date 2006/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Related

• 4-manifolds with a given boundary
• Extending Fibrations of the 3-Torus and Applications to Torus Surgery in 4-Manifolds
• Surgical invariants of four-manifolds
• Borromean surgery equivalence of spin 3-manifolds with boundary
• 3-manifolds lying in trisected 4-manifolds