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

Hakho Choi; Jongil Park; Ki-Heon Yun

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

Geometric Topology 2017-04-25 v3

Authors: Hakho Choi , Jongil Park , Ki-Heon Yun

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

smooth 4-manifolds dehn surgery exotic manifolds

Cite

@article{arxiv.1704.02181,
  title  = {On dissolving knot surgery $4$-manifolds under a $\mathbb{CP}^2$-connected sum},
  author = {Hakho Choi and Jongil Park and Ki-Heon Yun},
  journal= {arXiv preprint arXiv:1704.02181},
  year   = {2017}
}

Comments

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

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

Abstract

Keywords

Cite

Comments

Related papers