On dissolving knot surgery $4$-manifolds under a ${\mathbb{CP}}^2$-connected sum

Abstract

In this article we prove that, if $X$ is a smooth $4$-manifold containing an embedded double node neighborhood, all knot surgery $4$-manifolds $X_K$ are mutually diffeomorphic to each other after a connected sum with ${\mathbb{CP}}^2$. Hence, by applying to the simply connected elliptic surface $E(n)$, we also show that every knot surgery $4$-manifold $E(n{)}_K$ is almost completely decomposable.

14 pages, 24 figures; Introduction is rewritten. A remark is added

References in corpus (2)

• On infinite order corks
• Infinite order corks via handle diagrams