Uniqueness of contractible coboundary (Ex)
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| − | Let $\Sigma$ be a homology 3-spheres. If $\Sigma$ is the boundary of compact, contractible 4-manifolds $\Omega_1$ and $\Omega_2$ show there is a homeomorphism $\Omega_1 \to \Omega_2$ which is the identity on the boundary. (Hint: You may have to use the h-cobordism theorem for manifolds with boundary. | + | Let $\Sigma$ be a homology 3-spheres. If $\Sigma$ is the boundary of compact, contractible 4-manifolds $\Omega_1$ and $\Omega_2$ show there is a homeomorphism $\Omega_1 \to \Omega_2$ which is the identity on the boundary. (Hint: You may have to use the h-cobordism theorem for manifolds with boundary.) |
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[[Category:Exercises]] | [[Category:Exercises]] | ||
[[Category:Exercises without solution]] | [[Category:Exercises without solution]] | ||
Latest revision as of 06:27, 10 January 2019
Let 
be a homology 3-spheres. If is the boundary of compact, contractible 4-manifolds 
and 
show there is a homeomorphism 
which is the identity on the boundary. (Hint: You may have to use the h-cobordism theorem for manifolds with boundary.)
