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

Hakho Choi; Jongil Park; Ki-Heon Yun

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arXiv · 1704.02181

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

Hakho Choi·Jongil Park·Ki-Heon Yun

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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.

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Hakho Choi, Jongil Park, Ki-Heon Yun. 2017-04-07. On dissolving knot surgery $4$-manifolds under a $\mathbb{CP}^2$-connected sum. https://arxiv.org/abs/1704.02181

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