# Tagged Questions

**10**

votes

**0**answers

155 views

### Fox re-imbedding theorem in dimension four

Fox re-imbedding theorem states the following:
A compact 3-manifold $M$ with boundary that embeds in the three-sphere $S^3$, can be re-imbedded in $S^3$ so that its complement is a union of ...

**4**

votes

**1**answer

234 views

### Casson invariant and signature

In W. Neumann, J. Wahl, "Casson invariant of links of singularities",
Comment. Math. Helv.,1990, Vol. 65, Issue 1, pp 58-78 some connection between the Casson invariant and the signature is ...

**5**

votes

**5**answers

977 views

### What is the possible usefulness of étale topology and cohomology apart from the resolution of the Weil conjecture ?

My question is as stated in the title:
What is the possible usefulness of étale topology and cohomology apart from the resolution of the Weil conjecture ?
I am particularly interested to know if ...

**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 ...

**10**

votes

**1**answer

571 views

### Where are $+$, $-$ and $\infty$ in bordered Heegaard-Floer theory?

Here goes my first MO-question. I've just read Lipshitz, Ozsváth and Thurston's recently updated "A tour of bordered Floer theory". To set the stage let me give two quotes from this paper.
...

**10**

votes

**2**answers

384 views

### Embedding the product of three circles in the 4-sphere.

Let $M$ be a smooth submanifold of the 4-sphere $S^4$. I'm going to demand that $M$ be diffeomorphic to $S^1 \times S^1 \times S^1$. By Jordan-Brouwer separation, $M$ separates the 4-sphere into ...

**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.
...

**21**

votes

**4**answers

1k views

### Can all n-manifolds be obtained by gluing finitely many blocks?

Fix a dimension $n\geqslant 2$. Let $S= \{M_1,\ldots, M_k\}$ be a finite set of smooth compact $n$-manifold with boundary. Let us say that a smooth closed $n$-manifold is generated by $S$ if it may ...

**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 ...