# Showing that a 4-manifold obtained by attaching a 2-handle is simply-connected

I am reading Lemma 2.1 of this paper (https://arxiv.org/pdf/2012.12587.pdf) and I can't see why $$W$$ is simply-connected. Here is the situation:

Let $$K$$ be a ribbon knot in $$S^3$$; it bounds a ribbon disk $$D$$ in $$B^4$$. Let $$Y$$ be the 3-manifold obtained by 0-surgery on $$K$$. Let $$\nu D$$ be a closed tubular neighborhood of $$D$$ in $$D^4$$ and let $$X=B^4-\text{int} (\nu D)$$. Then we have $$\partial X=Y$$ (Boundary of slice disk exterior is the zero surgery of slice knot). Now let $$J$$ be an arbitrary knot in $$Y$$, let $$Y'$$ be the 3-manifold obtained from $$Y$$ by an integral Dehn surgery on $$J$$, and suppose that $$Y'$$ is an integral homology $$S^3$$.

The lemma is claiming that $$Y'$$ bounds a contractible 4-manifold $$W$$, and in the proof $$W$$ is constructed by attaching a 2-handle to $$X$$ along $$J$$ (with the same framing coefficient with surgery coefficient.) In the second paragraph of the proof, there is the following statement: "$$W$$ must be simply-connected if the resulting 3-manifold is a homology sphere." Here the resulting 3-manifold is $$Y'$$ and it is assumed to be a homology sphere, so this means that $$W$$ is simply-connected, but I can't see why. How can we show this?

What I know is that $$W$$ is a homology 4-ball, and $$X$$ has the homology of $$S^1\times B^3$$. Also from van Kampen's theorem applied to $$B^4=X\cup \nu D$$, $$\pi_1(X)$$ is normally generated by the class of $$\{\text{pt.}\}\times \partial D^2 \subset D\times D^2 =\nu D$$. Finally, by van Kampen's theorem applied to $$W=X\cup h$$ ($$h$$ is the 2-handle), $$\pi_1(W)$$ is the quotient of $$\pi_1(X)$$ by the subgroup normally generated by the class of the knot $$J$$.