If a closed surface is embedded in the 3-sphere, then does it bound a handlebody?
2026-03-25 13:05:07.1774443907
Does a closed surface in the 3-sphere bound a handlebody?
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Not necessarily. Start with a sphere and add a knotted tube on the inside and a knotted tube on the outside. This is a genus two surface that does not bound a handlebody.