All Questions
11 questions
4
votes
0
answers
161
views
Question on the construction of transversely oriented foliation on a sutured 3-manifold
The question is based on the proof of the main theorem of Gabai's paper on Foliations and the topology of 3-manifolds which is the following:
Theorem 5.1. Suppose $M$ is connected, and $(M,\gamma)$ ...
3
votes
1
answer
173
views
Do taut foliations leafwise branch covering S^2 yield foliations by circles?
In this paper, Danny Calegari shows that taut foliations in (let's say closed for simplicity) 3-manifolds are precisely those which admit a map $f: M \to S^2$ which restricts to a branched cover on ...
- 187
10
votes
0
answers
288
views
Contact structures associated to taut foliations
Eliashberg and Thurston showed that a taut foliation may be deformed to tight (positive and negative) contact structures. Vogel proved that for a taut foliation without torus leaves, the associated ...
- 68.9k
4
votes
0
answers
172
views
Survey or good reference of taut foliations
I am interested in the topology of foliations.
In particular, I want to understand taut foliations, or projectively Anosov flows, and Anosov flows.
I guess that
A. Candel and L. Conlon, Foliations I (...
- 73
5
votes
1
answer
249
views
Which elements of the fundamental group can be realized as transversals of a taut foliation?
Specifically in a closed, orientable 3-manifold. I'm not necessarily looking for a complete answer, as I don't expect one. Is there prior literature on this question? Also interested in this question ...
- 187
12
votes
0
answers
281
views
3-manifold foliated by circles is Seifert fibered
Let $M$ be a compact 3-manifold with boundary equipped with a 1-dimensional foliation all of whose leaves are circles. An old theorem of Epstein says that $M$ is a Seifert fibered space.
The proof of ...
- 121
8
votes
1
answer
372
views
1-Bridge Braids in Solid Tori (Berge-Gabai knots), dual knots, & knot exteriors
Let $K$ be a knot in a solid torus. Combining results of Berge and Gabai, we know that if $K$ admits a solid torus surgery, then $K$ is a 1-bridge braid. Using Gabai's result, we can figure out what ...
- 561
8
votes
2
answers
704
views
Taut foliations and closed leaves
EDITED
A codimension-1 foliation $\mathcal{F}$ of a (closed, connected, oriented) 3-manifold is taut if there exists a simple closed curve $\gamma$ that intersects each leaf of $\mathcal{F}$ ...
- 561
16
votes
1
answer
632
views
Three-manifolds having a Reebless foliation but not a taut one
A straightforward argument reveals that a taut foliation is Reebless, and of course there are many examples of Reebless foliations that are not taut. I guess that there are many examples of three-...
- 606
1
vote
1
answer
154
views
On the realization of a compact surface as a leaf of an analytic foliation
Let $S$ be a compact orientable surface of genus $g \geq 2$. Is there any transversely real (or complex) analytic codimension one foliation $\mathcal{F}$ such that $\mathcal{F}$ has $S$ as a leaf with ...
13
votes
1
answer
2k
views
Question about Thurston's paper "A norm for the homology of 3-manifolds"
I have a question about the proof of Theorem 5 in Thurston's paper "A norm for the homology of 3-manifolds". It's the theorem that asserts that the fibered faces are, well, fibered. More precisely, ...
- 133