All Questions
8 questions
19
votes
6
answers
3k
views
Diffeomorphism of 3-manifolds
Surgery theory aims to measure the difference between simple homotopy types and diffeomorphism types. In 3 dimensions, geometrization achieves something much more nuanced than that. Still, I wonder ...
- 13.2k
13
votes
2
answers
534
views
Heegaard splitting of covering hyperbolic manifold.
I am curious about how the Heegaard genus changes after a finite covering.
Is there anyone constructing an closed hyperbolic 3-manifold $N$ such that
the Heegaard genus of a finite covering of $N$ ...
- 841
9
votes
1
answer
605
views
Mapping Class Groups and torus (JSJ) decomposition of closed 3-manifolds
I am wondering if some intuitive relation exists between Mapping Class Group (MCG) of a 3-manifold (assume "simple" enough manifolds: closed,compact,irreducible, orientable, non-hyperbolic) and its ...
- 231
6
votes
1
answer
1k
views
Dehn surgery on handlebody
Assume $V$ is a handlebody and $C$ be a simple closed curve contained in the interior of $V$.
As Sam said, there exists some simple closed curve such that every dehn surgery along it produces a ...
- 841
6
votes
1
answer
324
views
Computation of $\pi_1$ for a Mazur manifold and its boundary
If we attach a $4$-dimensional $1$-handle $D^1 \times D^3$ to a $4$-dimensional $0$-handle $B^4$, we obtain $S^1 \times D^3$. The null homologous knot in $S^1 \times S^2$ indicated in the picture ...
- 606
4
votes
2
answers
536
views
Explicit tetrahedralizations of closed 3-manifolds and connections between convex polytopes and hyperbolic knot complements
There are three consistent ways to glue opposite faces of a dodecahedron to get a closed 3-manifold. With a $\frac{1}{10}$ twist we receive the Poincaré dodecahedral space, with a $\frac{3}{10}$ twist ...
- 1,441
3
votes
3
answers
769
views
Reducible 3d torus bundles
Here reducible means that the mapping class for the fiber is a reducible auto-homeomorph in the sense of Nielsen-Thruston. So,
could anyone give me a hint to classify them?
In contrast, do you agree ...
- 345
2
votes
2
answers
552
views
Is the following 3-manifold irreducible?
We start with product manifold $ X := S_g \times (0,1)$, where $S_g$ is a closed, orientable surface of genus $g \geq 1$. Since this has $\mathbb R^3$ as its universal cover, $X$ is irreducible. Now $...
- 1,255