# Every h-cobordism embeds into $M times I$?

Suppose we are in high dimension. By the s-cobordism theorem, any h-cobordism has an inverse given by a h-cobordism with the inverse torsion. Thus we have a isomorphism from the composite to the trivial h-cobordism. Thus by, restriction we can embed our h-cobordism into $$M times I$$.

Is there a simple handle manipulation argument that doesn’t use the full force of the s-cobordism theorem? Does it work in low dimensions?

Mathematics Asked by Connor Malin on November 14, 2021

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