# Tagged Questions

**4**

votes

**1**answer

313 views

### On the fundamental group of closed 3-manifolds

I know that every finitely presented group can be realized as the fundamental group of a compact, connected, smooth manifold of dimension 4 (or higher). In dimension 2 there are strong restriction on ...

**11**

votes

**1**answer

564 views

### Manifolds with prescribed fundamental group and finitely many trivial homotopy groups

Fix $G$, a finitely generated presented group.
It is known that for every $k > 3$ there is a closed $k$-manifold whose fundamental group is $G$. Similarly, there is a topological space with ...

**11**

votes

**0**answers

474 views

### Codimension Two Embeddings in Goodwillie-Weiss Manifold Calculus, and the Difficulty of Fundamental Groups

In manifold calculus, there are various analyticity estimates which run into trouble for codimension two embeddings. For instance, the functor $\operatorname{Emb}(M,N)$ is analytic in $M$ if $\dim M ...