Nonexistence of twists and surgeries generating exotic 4-manifolds

2016/10/13 by Kouichi Yasui, Yasui, Kouichi
Mathematics · #57R17 #57R55 #57R65 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1610.04033

openalex publication_date 2016/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is well known that for any exotic pair of simply connected closed oriented 4-manifolds, one is obtained from the other by twisting a compact contractible submanifold via an involution on the boundary. By contrast, here we show that for each positive integer n, there exists a simply connected closed oriented 4-manifold X such that, for any compact (not necessarily connected) codimension zero submanifold W with b₁(∂ W)

Citations

• Akbulut's corks and h-cobordisms of smooth simply connected 4-manifolds
• Corks, exotic 4-manifolds and knot concordance
• Contact 5-manifolds and smooth structures on Stein 4-manifolds
• On infinite order corks
• Non-existence theorems on infinite order corks

Related

• From zero surgeries to candidates for exotic definite four-manifolds
• Absolutely exotic compact 4-manifolds
• Exotic 4-manifolds with signature zero
• A plug with infinite order and some exotic 4-manifolds
• Smooth structures on non-orientable four-manifolds and free involutions