Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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


Author: David Gillman
Journal: Proc. Amer. Math. Soc. 110 (1990), 829-834
MSC: Primary 57N10; Secondary 57M40, 57Q65
MathSciNet review: 1021898
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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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DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1021898-6
Article copyright: © Copyright 1990 American Mathematical Society