# Tagged Questions

**20**

votes

**4**answers

1k views

### Algorithmically unsolvable problems in topology

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 ...

**3**

votes

**1**answer

744 views

### Homology is computable because it is stable under suspension

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 ...

**8**

votes

**1**answer

340 views

### 4-manifolds in the 4-sphere such that it, *and* its complement have unsolvable word problem

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 ...

**18**

votes

**1**answer

741 views

### Word problem for fundamental group of submanifolds of the 4-sphere

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 ...

**10**

votes

**3**answers

711 views

### Which properties of finite simplicial sets can be computed?

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 ...