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Jayq
Jayq
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My question arose when I was working on a research problem. It is as following:

Let $M$ be a homology manifold whose homology groups are the same as a sphere. Assume further that the double suspension of $M$ is homeomorphic to a sphere. Is $M$ homeomorphic to the suspension of a homology sphere?

Edition: Is $M$ homeomorphic to either suspension of a homology sphere or homeomorphic to a homology sphere.

My question arose when I was working on a research problem. It is as following:

Let $M$ be a homology manifold whose homology groups are the same as a sphere. Assume further that the double suspension of $M$ is homeomorphic to a sphere. Is $M$ homeomorphic to the suspension of a homology sphere?

My question arose when I was working on a research problem. It is as following:

Let $M$ be a homology manifold whose homology groups are the same as a sphere. Assume further that the double suspension of $M$ is homeomorphic to a sphere. Is $M$ homeomorphic to the suspension of a homology sphere?

Edition: Is $M$ homeomorphic to either suspension of a homology sphere or homeomorphic to a homology sphere.

Source Link
Jayq
Jayq
  • 377
  • 1
  • 5

"Inverse" of Double Suspension Theorem

My question arose when I was working on a research problem. It is as following:

Let $M$ be a homology manifold whose homology groups are the same as a sphere. Assume further that the double suspension of $M$ is homeomorphic to a sphere. Is $M$ homeomorphic to the suspension of a homology sphere?