On the topology of a Boolean representable simplicial complex. (English) Zbl 1358.05316
Summary: It is proved that the fundamental groups of Boolean representable simplicial complexes (BRSC) are free and the rank is determined by the number and nature of the connected components of their graph of flats for dimension . In the case of dimension 2, it is shown that BRSC have the homotopy type of a wedge of spheres of dimensions 1 and 2. Also, in the case of dimension 2, necessary and sufficient conditions for shellability and being sequentially Cohen-Macaulay are determined. Complexity bounds are provided for all the algorithms involved.
MSC:
| 05E45 | Combinatorial aspects of simplicial complexes |
| 05B35 | Combinatorial aspects of matroids and geometric lattices |
| 14F35 | Homotopy theory and fundamental groups in algebraic geometry |
| 15B34 | Boolean and Hadamard matrices |
| 55P15 | Classification of homotopy type |
| 55U10 | Simplicial sets and complexes in algebraic topology |
| 57M05 | Fundamental group, presentations, free differential calculus |
Keywords:
simplicial complex; matroid; Boolean representation; fundamental group; shellability; sequentially Cohen-Macaulay; EL-labeling; homotopy typeReferences:
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