Questions tagged [incompressible-surfaces]
The incompressible-surfaces tag has no usage guidance.
9
questions
2
votes
0
answers
114
views
Non Seifert incompressible surfaces detected by ideal points
Given a 3-manifold with toric boundary, the Culler-Shalen theory associates an incompressible surface to any ideal point of its character variety. From the proof of the Neuwirth conjecture, one knows ...
- 223
9
votes
1
answer
791
views
On the geometrization of double branched covers
I recently got into Lickorish's paper Prime knots and tangles and a question, which I didn't have the first time I read it, naturally emerged.
The Thurston-Perelman Geometrization Theorem asserts ...
- 576
4
votes
1
answer
131
views
the local structure of an immersed incompressible surface
Assume that $M$ is a closed, irreducible, orientable 3-manifold. Suppose that we have a closed, immersed, incompressible surface $F$ of genus at least 1. Since we only required $F$ to be immersed in $...
- 799
4
votes
1
answer
202
views
Constructing a "nice" cobordism
Denote by $\Sigma_g$ the closed, orientable surface of genus $g$. I want to construct a cobordism $M_g$ between $\Sigma_g$ and $\Sigma_{g+1}$ with the following two nice properties:
1) $M_g$ is an ...
- 1,215
13
votes
1
answer
500
views
Geometric intersection with incompressible surfaces
Let $M$ be a oriented compact $3$-manifold, closed or with boundary.
For any incompressible surface $F$, define a function $i_F$ on the set of homotopy classes of closed curves in $M$ by $$i_F (\alpha)...
- 482
9
votes
3
answers
877
views
Is there a way to classify incompressible surfaces in $\Sigma \times [0,1]$ ?
Is there a way to classify incompressible surfaces in $\Sigma \times [0,1]$ where $\Sigma$ is any closed surface? I know of the Hatcher-Thurston classification of incompressible surfaces in 2-bridge ...
15
votes
1
answer
645
views
compressibility of Seifert surface after 0-surgery
Gabai's solution of the Property R conjecture shows that a minimal genus Seifert surface of a knot, capped off in the 0-framed surgery along that knot, is of minimal genus in its homology class. In ...
- 18.4k
3
votes
1
answer
225
views
Example of hyperbolic 3-fold with no embedded incompressible subsurfaces
Kahn-Markovic show that every hyperbolic 3-fold contains
an immersed $\pi_1$ injective surface. Are there any known examples
of hyperbolic 3-folds that do not contain a embedded $\pi_1$ injective
...
- 624
13
votes
1
answer
2k
views
Incompressible surfaces in an open subset of R^3
Let $U$ be a connected open subset of $\mathbb R^3$. Furthermore, we have:
$\mathbb R^3\setminus U$ has exactly two connected components (thus by Alexander duality, $H_2(U;\mathbb Z)=\mathbb Z$).
$U$...
- 17.8k