Milnor's homotopy-sphere conjecture for Brieskorn manifolds

Let $a_0, a_1,\dots,a_n\geq 2$, and let

$$K(a_0,a_1,\dots,a_n)=\{x_0^{a_0}+x_1^{a_1}+\dots+x_n^{a_n}=0\}\cap \mathbf{S}^{2n+1}$$

be the $(2n-1)$-dimensional Brieskorn link. Let $\Gamma(a_0,a_1,\dots,a_n)$ be the graph with vertices $0,1,\dots,n$, joining $i$ and $j$ when $\gcd(a_i,a_j)>1$. Milnor's conjecture. For $n\geq 3$, the link $K(a_0,a_1,\dots,a_n)$ is a homotopy $(2n-1)$-sphere if and only if $\Gamma(a_0,a_1,\dots,a_n)$ has at least two isolated points, or has one isolated point and at least one connected component $\Gamma'$ with an odd number of vertices such that $\gcd(a_i,a_j)=2$ for all distinct vertices $i,j\in\Gamma'$. This gives a combinatorial criterion for recognizing when Brieskorn links are homotopy spheres; the source presents it as a conjecture of Milnor, and no resolution is supplied in the provided text.