My question is about the Alexander polynomial of a slice knot.

For a slice knot $K$, Fox-Milnor and Terasaka proved that $$ \Delta_{K}(t) \doteq f(t) f(t^{-1})$$ for some polynomial $f(t) \in \mathbb{Z}[t]$, where $\Delta_{K}(t)$ is the Alexander polynomial of $K$ and $\doteq$ means up to units of $\mathbb{Z}[t, t^{-1}]$.

Let $D$ be a slice disk for $K$. Then a folklore result states that $$f(t) \doteq \Delta_{D}(t),$$ where $ \Delta_{D}(t)$ denotes the Alexander polynomial of $D$.

$\textbf{Question 1.} $ Is there a reference of this folklore result ?

Note that this folklore result is important when we calculate the Alexander polynomial of a ribbon knot $R$. Indeed, let $D$ the slice disk in the $4$-ball $B^4$ obtained from a ribbon presentation of $R$. Then we easily obtain the presentation of $\pi_{1}(B^4 \setminus N(D))$ and can determine $ \Delta_{D}(t)$ using Fox calculus, where $N(D)$ is a tubular neighborhood of $D$.

I heard from Akio Kawauchi (who was my adviser) that this folklore result is true, at least, for ribbon knots and he did not know any references. His proof is using the Blanchfield duality (I do not follow the proof fully).

There is another question. Here recall the Reidemeister torsion. Let $K$ be a knot in $S^3$ and $\tau_{\alpha}(S^3 \setminus N(K))$ the Reidemeister torsion associated to the abelian map $\alpha$ of $\pi_{1}(S^3 \setminus N(K) )$. (Precisely, $\alpha : \pi_{1}(S^3 \setminus N(K) ) \to GL(1; \mathbb{Q}(t)).$) Milnor's theorem states that $$ \tau_{\alpha}(S^3 \setminus N(K)) \doteq \dfrac{\Delta_K(t)}{t-1}$$ Let $D$ be a slice disk for some knot and $\tau_{\alpha}((B^4 \setminus N(D)))$ be the Reidemeister torsion of a slice disk $D$ associated to the abelian map $\alpha$ of $\pi_{1}(B^4 \setminus N(D) )$.

$\textbf{Question 2.} $ Is it true that $$ \tau_{\alpha}(B^4 \setminus N(D))\doteq \dfrac{\Delta_D(t)}{t-1} \ ?$$

It seems that, if the Whitehead group of $\pi_{1}(B^4 \setminus N(D))$ is trivial, then Question 2 is true.

$\textbf{Question 3.} $ Is the Whitehead group of $\pi_{1}(B^4 \setminus N(D))$ trivial ?

Finally, note that I am not familiar with the Reidemeister torsion and the Whitehead group, and therefore there might exist some wrong descriptions. If so, please tell me !