Knot surgery $4$-manifolds $E(n)_K$ without $1$- and $3$-handles

Ju A Lee; Ki-Heon Yun

Knot surgery $4$-manifolds $E(n)_K$ without $1$- and $3$-handles

Geometric Topology 2026-01-19 v1

Authors: Ju A Lee , Ki-Heon Yun

Abstract

In this article, we demonstrate that for any positive integer $n$ , the knot surgery $4$ -manifold $E(n)_K$ has a handle decomposition without $1$ - and $3$ -handles. Here, $K$ represents either a fibered two-bridge knot $C(2\epsilon_1, 2\epsilon_2,\cdots, 2\epsilon_{2g})$ ( $\epsilon_i \in \{ 1, -1\}$ ) in Conway's notation or a Stallings knot $K_m$ ( $m \in \mathbb{Z}$ ).

Keywords

4-manifold knot surgery handle decomposition two-bridge knot Stallings knot

Cite

@article{arxiv.2601.11211,
  title  = {Knot surgery $4$-manifolds $E(n)_K$ without $1$- and $3$-handles},
  author = {Ju A Lee and Ki-Heon Yun},
  journal= {arXiv preprint arXiv:2601.11211},
  year   = {2026}
}

Comments

14 pages, 7 figures

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