Relating CAT(0) cubical complexes and flag simplicial complexes

Relating CAT(0) cubical complexes and flag simplicial complexes

Given a finite CAT(0) cubical complex, we define a flag simplicial complex associated to it, called the crossing complex. We show that the crossing complex holds much of the combinatorial information of the original cubical complex: for example, hyperplanes in the cubical complex correspond to verte...

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Bibliographic Details
Published in:Advances in applied mathematics Vol. 147; p. 102502
Main Author: Rowlands, Rowan
Format: Journal Article
Language:English
Published: Elsevier Inc 01-06-2023
Subjects:
secondary
primary
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Summary:Given a finite CAT(0) cubical complex, we define a flag simplicial complex associated to it, called the crossing complex. We show that the crossing complex holds much of the combinatorial information of the original cubical complex: for example, hyperplanes in the cubical complex correspond to vertex links in the crossing complex, and the crossing complex is balanced if and only if the cubical complex is cubically balanced. The most significant result is that the sets of f-vectors of CAT(0) cubical complexes and flag simplicial complexes are equal, up to an invertible linear transformation.
ISSN:0196-8858
1090-2074
DOI:10.1016/j.aam.2023.102502