Non-constructible complexes and the bridge index (Q5942868)
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scientific article; zbMATH DE number 1643797
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Non-constructible complexes and the bridge index |
scientific article; zbMATH DE number 1643797 |
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Non-constructible complexes and the bridge index (English)
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13 October 2002
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non-constructible balls and spheres
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A simplicial complex is constructible if it can be recursively constructed as the union of constructible complexes with a constructible intersection. Constructibility is strictly weaker than shellability.NEWLINENEWLINENEWLINEThe authors prove that a \(3\)-dimensional polytopal ball or sphere is not constructible provided its \(1\)-skeleton contains a knot~\(K\) whose bridge number exceeds the number of edges of~\(K\). From this result the authors derive that for each \(d\geq 3\) there exists a simplicial PL-sphere whose cubical barycentric subdivision is not constructible.
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