Abstract
A cell partitioning of a closed 3 3 -manifold M 3 {M^3} is a finite covering of M 3 {M^3} by 3 3 cells that fit together in a bricklike pattern. A cell partitioning H H of M 3 {M^3} is shellable if H H has a counting âš h 1 , h 2 , ⊠, h n â© \langle {h_1},{h_2}, \ldots ,{h_n}\rangle such that if 1 â©œ i > n , h 1 âȘ h 2 âȘ ⯠âȘ h i 1 \leqslant i > n,\;{h_1} \cup {h_2} \cup \cdots \cup {h_i} is a 3 3 -cell. The main result of this paper is a relationship between nonshellability of a cell partitioning H H of S 3 {S^3} and the existence of links in S 3 {S^3} specially related to H H . This result is used to construct a nonshellable cell partitioning of S 3 {S^3} .
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