This question is inspired by a paper by B. Poonen that appeared on the arxiv some time ago: http://arxiv.org/abs/1204.0299. The paper gives a sample of algorithmically unsolvable problems from various ...
I've heard it said that the reason why the homology groups of a space are a computable invariant is because they are a stable invariant in the sense that they are stable under suspension. I'm ...
In an earlier thread I had asked whether or not one can find a smooth 4-dimensional submanifold of $S^4$ whose fundamental group has an unsolvable word problem. The answer is yes, and the reference ...
Given any finitely-presented group $G$, there are a few equivalent techniques for constructing smooth/PL 4-manifolds $M$ such that $\pi_1 M$ is isomorphic to $G$. For most constructions of these ...
A simplicial set $X$ is a a combinatorial model for a topological space $|X|$, its realization, and conversely every topological space is weakly equivalent to such a realization of a simplicial set. I ...