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

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 $C(2ε_1, 2ε_2,\cdots, 2ε_{2g})$ ($ε_i \in \{ 1, -1\}$) in Conway's notation or a Stallings knot $K_m$ ($m \in \mathbb{Z}$).

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