# Tagged Questions

**3**

votes

**1**answer

227 views

### What are Kirby diagrams of candidate exotic 4-manifolds?

It is an open problem whether there exist smooth manifolds homeomorphic, but not diffeomorphic to the standard $S^4$. The same is true for the 4-torus and several other manifolds. Handle ...

**6**

votes

**0**answers

182 views

### What is the state of the art in 4-manfold 2-types?

In an old answer to an old question of mine, Peter Teichner commented that it is an open problem to determine which homotopy 2-types arise from 4-manifolds. In some instances we know that a 4-manifold ...

**4**

votes

**1**answer

418 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 ...

**13**

votes

**0**answers

206 views

### Shortest Casson tower containing a slice disk for the attaching curve

A Casson tower is obtained as follows: Start with a properly immersed disk in $\mathbb{B}^4$ - a regular neighborhood of such a disk is called a kinky handle. The boundary of the core disk ...

**11**

votes

**2**answers

448 views

### Existing proofs of Rokhlin's theorem for PL manifolds

I'm looking for a comprehensive reference to existing proofs of Rokhlin's theorem that a 4-dimensional closed spin PL manifold has signature divisible by 16.
I'm specifically interested in direct ...

**5**

votes

**2**answers

522 views

### First appearance of Novikov's additivity theorem

Hi!
Novikov's additivity theorem states that if you glue together two compact oriented 4n-manifolds along a connected component of their boundaries, the signature of the resulting manifold is ...

**2**

votes

**2**answers

357 views

### Reference for the proof of this statement?

Can anyone give me the reference for this statement?:
Let $M$ be a closed oriented smooth 4-manifold. Any element $a\in H_2(M)$ can be represented by a smoothly embedded, oriented surface.
I found ...

**57**

votes

**8**answers

5k views

### Theoretical physics: Why not just R^4?

You and I are having a conversation:
"Okay," I say,"I think I get it. The gauge groups we know and love arise naturally as symmetries of state spaces of particles."
"Something like that"
"...And ...