Yet another classic, at last found its way to my library.

I'm wondering. If #computability and #unsolvability theories are mostly concerned with the existence of algorithms for classes of problems, if one could prove or disprove such a thing (class of theorems?) starting from #geometry.

I'll explain. I've recently understood (Steenrod et al, "First concepts of topology") that #topology is mostly concerned in proving existence theorems. The subject matter of this book sounds, in a way, like an attempt to prove such theorems. So naturally I came to wonder if anyone had attempted tackling them with topological means and tools instead. I haven't looked to see if this question even makes sense, but my humble instinct says that maybe yes, and that most likely at least someone has worked on it in the past.