Talk:Integral homology 3-spheres embed in the 4-sphere (Ex)
From Manifold Atlas
Let be a homology
-sphere. By Freedman, there exists a (unique) contractible topological
-manifold
with
.
![W:=\Omega\cup_{Y\times I}(-\Omega)](/images/math/9/f/2/9f2bef8e0960cff4cf0b0c6af7bf9c13.png)
![Y](/images/math/3/9/a/39abfebb66c060cd7541c76ff73c12da.png)
![\pi_1(\Omega)=0](/images/math/1/0/e/10e67bbc366a3fbd20ec0c74b60c9937.png)
![\pi_1(W)=0](/images/math/e/5/e/e5e293c333be5d6b4d1fe35d8037b0db.png)
![\tilde{H}_*(\Omega)=0](/images/math/7/5/7/75732ceab65c0eec44f563bce5e85e5a.png)
![\tilde{H}_*(\Omega\cap -\Omega)=\tilde{H}_*(Y)=0](/images/math/d/f/1/df1c8f058f54af0e40f8dfded0680583.png)
![\tilde{H}_*(W)=0](/images/math/2/b/4/2b403c2960579a88ac29d7e40337a666.png)
![H_2(W)=0](/images/math/4/c/a/4caf8749e3b460a9d7b2046d0599b729.png)
![W](/images/math/d/d/9/dd9cfece1f436d778e11355f768fd33e.png)
![S^4](/images/math/5/7/d/57d9b7e80fa0cbb5ad5af8a310aee97c.png)
Tex syntax erroris a (topological) embedding of
![Y](/images/math/3/9/a/39abfebb66c060cd7541c76ff73c12da.png)
![S^4](/images/math/5/7/d/57d9b7e80fa0cbb5ad5af8a310aee97c.png)