The 4-manifolds tag has no wiki summary.

**65**

votes

**4**answers

6k views

### How can there be topological 4-manifolds with no differentiable structure?

This is a very naive question, and I'm hoping that it will be matched by a correspondingly elementary answer. It is well known that not every topological 4-manifold admits a smooth structure. So ...

**12**

votes

**1**answer

1k views

### A question on classification of almost complex structures on $4$-manifolds

I have a (basic?) question in topology.
Question 1. Is it possible to characterise compact $4$-manifolds $M^4$, such that almost complex structures on $M^4$ are uniquely defined up to homotopy by ...

**18**

votes

**0**answers

905 views

### When is a compact topological 4-manifold a CW complex?

Freedman's $E_8$-manifold is nontriangulable, as proved on page (xvi) of the Akbulut-McCarthy 1990 Princeton Mathematical Notes "Casson's invariant for oriented homology 3-spheres".
Kirby showed that ...

**4**

votes

**1**answer

508 views

### Relation of SW and Donaldson Invariant

My question is:
I am request for the reference that Is there any relationship between the Seiberg-Witten Invariant and Donaldson's Invariant? Or the relationship between Seiberg-Witten Moduli Space ...

**4**

votes

**1**answer

117 views

### 0-homologous surface bounds

Given a map $f : S \to M^4$ from a compact closed not necessarily connected oriented surface to a compact oriented 4-manifold, such that $f_*([S])$ is zero in $H_2(M)$, is there a compact oriented ...