For a subring $R⊂ \mathbb Q$, a knot $K⊂S^3$ is called $R$-slice if there exists an embedded disk $D$ in an $R$-homology $4$-ball $B$ such that $∂(B,D) = (S^3,K)$, see [Definition 1.3, KW16]. We say $K$ is rationally (resp. integrally) slice if $R= \mathbb Q$ (resp. $= \mathbb Z$).

In terms of crossing, the minimal example of rationally slice knot seems (probably is) figure-eight knot $4_1$, see [Theorem 4.16, Cha07].

The classical definition of is that a knot $K ⊂ S^3$ is slice if it bounds a smoothly embedded disk $D^2$ in the $4$-ball $B^4$. Again in terms of crossing, the minimal example of slice knot is unknot $0_1$.

My question is that is there any minimal example of integrally slice knot?

For a subring $R⊂ \mathbb Q$, a knot $K⊂S^3$ is called $R$-slice if there exists an embedded disk $D$ in an $R$-homology $4$-ball $B$ such that $∂(B,D) = (S^3,K)$, see [Definition 1.3, KW16]. We say $K$ is rationally (resp. integrally) slice if $R= \mathbb Q$ (resp. $= \mathbb Z$).

In terms of crossing, the minimal example of rationally slice knot seems (probably is) figure-eight knot $4_1$, see [Theorem 4.16, Cha07].

A knot $K ⊂ S^3$ is slice if it bounds a smoothly embedded disk $D^2$ in the $4$-ball $B^4$. Again in terms of crossing, the minimal example of slice knot is unknot $0_1$.

My question is that is there any minimal example of integrally slice knot?

For a subring $R⊂ \mathbb Q$, a knot $K⊂S^3$ is called $R$-slice if there exists an embedded disk $D$ in an $R$-homology $4$-ball $B$ such that $∂(B,D) = (S^3,K)$, see [Definition 1.3, KW16]. We say $K$ is rationally (resp. integrally) slice if $R= \mathbb Q$ (resp. $= \mathbb Z$).

In terms of crossing, the minimal example of rationally slice knot is figure-eight knot $4_1$, see [Theorem 4.16, Cha07].

The classical definition of is that a knot $K ⊂ S^3$ is slice if it bounds a smoothly embedded disk $D^2$ in the $4$-ball $B^4$.

  Again in terms of crossing, the minimal example of slice knot is unknot $0_1$.

My question is that is there any minimal example of integrally slice knot?

For a subring $R⊂ \mathbb Q$, a knot $K⊂S^3$ is called $R$-slice if there exists an embedded disk $D$ in an $R$-homology $4$-ball $B$ such that $∂(B,D) = (S^3,K)$, see [Definition 1.3, KW16]. We say $K$ is rationally (resp. integrally) slice if $R= \mathbb Q$ (resp. $= \mathbb Z$).

In terms of crossing, the minimal example of rationally slice knot seems (probably is) figure-eight knot $4_1$, see [Theorem 4.16, Cha07].

The classical definition of is that a knot $K ⊂ S^3$ is slice if it bounds a smoothly embedded disk $D^2$ in the $4$-ball $B^4$. Again in terms of crossing, the minimal example of slice knot is unknot $0_1$.

My question is that is there any minimal example of integrally slice knot?