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

Hakho Choi, Jongil Park, Ki-Heon Yun

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 e…