7
votes
Accepted
On the geometrization of double branched covers
As Ian Agol mentioned in his comment, the OP's question can be thought of in terms of the Orbifold Theorem. There are two (contemporaneous and) independent proofs of the Orbifold Theorem:
Daryl ...
- 5,259
5
votes
Accepted
$\partial$-incompressibility of a surface obtained when attaching a 2-handle to an irreducible 3-manifold produces a reducible 3-manifold
Suppose that $S$, the relevant boundary component of $M$, is a torus. Suppose that $G$ is the given essential two-sphere in the filled manifold $N$. We isotope $G$ to have minimal intersection with $...
- 28.2k
5
votes
Accepted
the local structure of an immersed incompressible surface
For the first question, if the map of the surface in the manifold is made generic, then the singular set will consist of just double and triple points, and will be a graph with vertices of valence six ...
- 68.9k
4
votes
Is there a way to classify incompressible surfaces in $\Sigma \times [0,1]$ ?
Since you are asking for incompressible but not $\partial$-incompressible, the classification is more complicated. As pointed out in Sam Nead's answer, the classification of incompressible and ...
- 68.9k
1
vote
Is there a way to classify incompressible surfaces in $\Sigma \times [0,1]$ ?
Please check this paper--http://comp.uark.edu/~yoav/kobayashi-qiu-wang.pdf.
In Proposition 1, they have proved that there are infinitely many incompressible surface based on a simple curve. So I ...
- 841
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