Can anyone explain this paper :? " The world problem: on the computability of the topology of 4-manifolds"

Question

Link to the paper is here: https://arxiv.org/pdf/gr-qc/0506019.pdf

The author explains that the problem of determining if two 4-manifold are related by a homeomorphism is undecidable. And that this is unique to four dimensions.

Can someone construct a sketch, and explain why it doesn't work in other in other dimensions. Or at least why it doesn't work in another dimension as an example.