alt Hacker NewsI think it's not even a valid critique of that and it's sort of playing games with what the definition of a singularity is to reach the claim that it's making. I think the topology of the singularity is not even a well defined question and certainly not well understood enough to bear the strong claims in the paper.
Unfortunately you are wrong. Everything the paper is saying about the singularity and its properties in GR, and more generally about the black hole solutions it describes, is well understood and has been for decades. The definition of "singularity" that the paper is using is perfectly fine, and its topology is perfectly well-defined. A good textbook treatment is that of Wald (1984).
Some of the things the paper points out are not emphasized in other sources, which is probably why the authors chose to write it. But there is nothing in the paper that is in the least questionable or ill-defined; it's all standard General Relativity as applied to the Schwarzschild and Kerr black hole solutions.