# Tagged Questions

**3**

votes

**3**answers

425 views

### Questions on 3-manifolds with a given boundary

I have the following question:
For a given two-dimensional Riemann surface $C$,
Is there a way to classify all topologically distinct
three-dimensional compact manifolds $M$ whose boundary is $C$,
...

**25**

votes

**3**answers

7k views

### Properly Discontinuous Action

When looking definition, and theorems related to Properly discontinuous action of a group $G$ on a topological space $X$, it is different in different books (Topology and Geometry-Bredon, Complex ...

**6**

votes

**2**answers

657 views

### Compact cover of a Hausdorff compact space

In his book "Riemannian Geometry" do Carmo cites the Hopf-Rinow theorem in chapter 7. (theorem 2.8). One of the equivalences there deals with the cover of the manifold using nested sequence of compact ...

**5**

votes

**1**answer

510 views

### How can we show the spaces $M_{g}(n)$ and $M_{g, n}$ are homotopy equivalent?

How can we prove that the moduli space,$M_{g}(n)$, of genus $g$ Riemann surface with $n$ boundary components is homotopy equivalent to $M_{g,n}$, that is ,the moduli space of genus $g$ Riemann surface ...