# Tagged Questions

**9**

votes

**1**answer

351 views

### Complexity of surfaces bounding knots in 4-ball and 3-sphere respectively

I'm interested in a complexity question related to problems like the slice-ribbon problem.
To be specific, if $K \subset S^3$ is a knot, it might be non-trivial yet still bound a smoothly-embedded ...

**25**

votes

**0**answers

895 views

### What is the three-dimensional hyperbolic volume of a four-manifold?

Every smooth closed orientable 4-manifold may be constructed via a handle decomposition. Before asking a couple of questions, I recall some well-known facts about handle-decompositions of 4-manifolds.
...

**7**

votes

**2**answers

1k views

### Slice knots and exotic $\mathbb R^4$

In the http://arxiv.org/abs/math/0606464v1 I read
"If you want to prove existence of exotic smooth structure on $\mathbb R^4$ you can do this if you are in
possession of a knot which is ...

**20**

votes

**3**answers

1k views

### How expensive is knowledge? Knots, Links, 3 and 4-manifold algorithms. [closed]

With geometrization, Rubinstein's 3-sphere recognition algorithm and the Manning algorithm, 3-manifold theory has reached a certain maturity where many questions are "readily" answerable about ...

**13**

votes

**2**answers

920 views

### topological “milnor's conjecture” on torus knots.

Here's a question that has come up in a couple of talks that I have given recently.
The 'classical' way to show that there is a knot $K$ that is locally-flat slice in the 4-ball but not smoothly ...

**6**

votes

**2**answers

542 views

### slice=ribbon generalization to higher genus + potential counterexamples to slice=ribbon.

I have two questions about the slice=ribbon conjecture.
(1) If a knot $K \hookrightarrow S^3$ has smooth slice genus $g$, you can ask if it bounds a smooth genus $g$ surface in $S^3 \times [0, ...

**4**

votes

**4**answers

564 views

### 4-genus of a 2-bridge link

How can we calculate the 4-genus of a link L? The 4-genus is defined to be the minimal genus of orientable surface bounded by L in B^4. Is there any routine method to calculate that?
Especially, any ...

**0**

votes

**1**answer

241 views

### If the 4-genus of a link is zero, is it a slice link?

An n-component slice link is a link that bounds n disjoint discs in B^4. And the 4-genus of a link is defined to be the minimal genus of orientable surfaces bounded by it in B^4.
My question is: if ...