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Results tagged with 4-manifolds
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user 50754
A smooth 4-manifold is a 4-manifold with a smooth structure. In dimension four, in marked contrast with lower dimensions, topological and smooth manifolds are quite different.
5
votes
1
answer
230
views
$\pi_1$ of 4-manifolds that "look like" disk bundles
Let $X$ be a smooth compact oriented 4-manifold with $\partial X=L(p,1)$, $H_2(X;\Bbb Z)=\Bbb Z$, $H_3(X; \Bbb Z)=0$ and the induced map $\pi_1(L(p,1)) \to X$ surjective. What are the possibilities fo …
- 773
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 …
- 773
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 …
- 773
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 …
- 773