The Poincaré conjecture is true in the product of any graph with a disk

Gillman, David

doi:10.1090/S0002-9939-1990-1021898-6

The Poincaré conjecture is true in the product of any graph with a disk
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by David Gillman

Proc. Amer. Math. Soc. 110 (1990), 829-834

DOI: https://doi.org/10.1090/S0002-9939-1990-1021898-6

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Abstract:

We prove that the only compact $3$-manifold-with-boundary which has trivial rational homology, and which embeds in the product of a graph with a disk, is the $3$-ball. This implies that no punctured lens space embeds in the product of a graph with a disk. It also implies our title. The proof relies on a general position argument which enables us to perform surgery.

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