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A three-manifold is a space that locally looks like Euclidean three-dimensional space
10
votes
Taut foliations and closed leaves
I'm assuming you meant homologically non-trivial. There are two very famous theorems of Gabai, which show up in quite a lot of places in 3-dimensional topology for constructing taut foliations (in par …
6
votes
1
answer
508
views
Distinguishing homology $S^1 \times S^2$'s which bound homotopy $S^1$'s
Due to Mazur, Akbulut and Kirby and many others, there are many examples of integer homology 3-spheres which bound contractible 4-manifolds given by attaching a single 2-handle to $S^1 \times D^3$ wh …
2
votes
contact surgery diagram on Brieskorn manifolds
Here's a partial answer that works when $p=2$. If $\Sigma (a_0,a_1, \dots ,a_n)$ is defined as the link of the the singularity $\sum z_i ^{a_i}$, the map $\pi_0:\Bbb C^{n+1}\to \Bbb C^n$ with $\pi_0(z …
7
votes
1
answer
472
views
Homology 3-sphere with a unique Stein-fillable contact structure
Are there any known examples of oriented integer homology 3-spheres $Y$ (besides $S^3$) which have exactly one Stein-fillable contact structure up to isotopy? Failing that, what are the known examples …