Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Links and nonshellable cell partitionings of $S^ 3$
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by Steve Armentrout
Proc. Amer. Math. Soc. 118 (1993), 635-639
DOI: https://doi.org/10.1090/S0002-9939-1993-1132848-9

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 ${S^3}$.
References
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Bibliographic Information
  • © Copyright 1993 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 118 (1993), 635-639
  • MSC: Primary 57N12; Secondary 57M25, 57M40
  • DOI: https://doi.org/10.1090/S0002-9939-1993-1132848-9
  • MathSciNet review: 1132848