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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Links and nonshellable cell partitionings of $ S\sp 3$


Author: Steve Armentrout
Journal: Proc. Amer. Math. Soc. 118 (1993), 635-639
MSC: Primary 57N12; Secondary 57M25, 57M40
MathSciNet review: 1132848
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Abstract: A cell partitioning of a closed $ 3$-manifold $ {M^3}$ is a finite covering of $ {M^3}$ by $ 3$cells that fit together in a bricklike pattern. A cell partitioning $ H$ of $ {M^3}$ is shellable if $ H$ has a counting $ \langle {h_1},{h_2}, \ldots ,{h_n}\rangle $ such that if $ 1 \leqslant i < n,\;{h_1} \cup {h_2} \cup \cdots \cup {h_i}$ is a $ 3$-cell. The main result of this paper is a relationship between nonshellability of a cell partitioning $ H$ of $ {S^3}$ and the existence of links in $ {S^3}$ specially related to $ H$. This result is used to construct a nonshellable cell partitioning of $ {S^3}$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1132848-9
PII: S 0002-9939(1993)1132848-9
Article copyright: © Copyright 1993 American Mathematical Society