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

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 $K_m$ ($m\in \mathbb{Z}$).

14 pages, 7 figures