Asian Journal of Mathematics

Volume 23 (2019)

Number 5

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

Pages: 735 – 748

DOI: https://dx.doi.org/10.4310/AJM.2019.v23.n5.a2

Authors

Hakho Choi (School of Mathematics, Korea Institute for Advanced Study, Seoul, South Korea)

Jongil Park (Department of Mathematical Sciences, Seoul National University, Seoul, South Korea; and the Korea Institute for Advanced Study, Seoul, South Korea)

Ki-Heon Yun (Department of Mathematics, SungshinWomen’s University, Seoul, South Korea)

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.

Keywords

almost completely decomposable, knot surgery $4$-manifold

2010 Mathematics Subject Classification

14J27, 57N13, 57R55

Full Text (PDF format)

Received 23 June 2017

Accepted 5 July 2018

Published 30 April 2020